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Here your best chance is to get your opponent to leave his anchor on your 1 point, with the intention of getting both his checkers on the bar.  Open up your bar point and hope he rolls a 6, giving you lots of return shots at his blot on your 1 and in your outfield.

Best move:  12/9 7/2 (not listed)

I think that 7/2-6/3 is better, as it adds more assets. If red gets a lucky roll of 6-6 and you have moved 12/9, you will have just 1 hunter blot, the hit one in 7 pt, to attack red's runners, but with 6/3, red will be forced to hit both checkers of 12pt and 7pt and thus white will has 2 hunters and this increases his chances of hitting. Also with 6/3, you can attack the future blot in 1pt, if red get's a 6 and escape one chacker.

This is my analysis and may be I am wrong, but i will play 7/2-6/3, as i trust GNUBG in almost every move it makes.

This should be some sort of reference position. Recycling checkers is an important thema. When the other player has crushed board (or bear-off board in this case), you lose nothing if you get your checkers send back. But you can win a lot by hitting more checkers or breaking anchor. Recycling is also used to ruin backgame players timing. I made a wrong quick vote here and forgot the whole thema.

I was SO proud to have actually got this one right too - tho' to be honest I suspected it was a very unusual one so I thought "outside the box".

    1. Rollout          12/9 7/2                     Eq.:  -0,052
       0,474 0,000 0,000 - 0,526 0,051 0,034 CL  -0,052 CF  -0,052
      [0,003 0,000 0,000 - 0,003 0,003 0,004 CL   0,006 CF   0,006]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055124781 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 8 more moves within equity 0,12
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]
    2. Rollout          13/8 7/4                     Eq.:  -0,056 ( -0,004)
       0,472 0,000 0,000 - 0,528 0,072 0,050 CL  -0,056 CF  -0,056
      [0,004 0,000 0,000 - 0,004 0,004 0,005 CL   0,007 CF   0,007]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055124781 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 8 more moves within equity 0,12
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]
    3. Rollout          13/10 7/2                    Eq.:  -0,060 ( -0,008)
       0,470 0,000 0,000 - 0,530 0,072 0,047 CL  -0,060 CF  -0,060
      [0,003 0,000 0,000 - 0,003 0,003 0,003 CL   0,006 CF   0,006]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055124781 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 8 more moves within equity 0,12
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]
    4. Rollout          7/2 6/3                      Eq.:  -0,077 ( -0,025)
       0,462 0,000 0,000 - 0,538 0,054 0,042 CL  -0,077 CF  -0,077
      [0,002 0,000 0,000 - 0,002 0,004 0,004 CL   0,005 CF   0,005]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055124781 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 8 more moves within equity 0,12
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]
    5. Rollout          7/4 7/2                      Eq.:  -0,085 ( -0,033)
       0,458 0,000 0,000 - 0,542 0,039 0,024 CL  -0,085 CF  -0,085
      [0,002 0,000 0,000 - 0,002 0,002 0,002 CL   0,005 CF   0,005]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055124781 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 8 more moves within equity 0,12
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]

for example, when i did these roll-outs, for the 0-ply recommended move 7/2 6/3 i got results that varied substantially from the 0-ply evaluation (Eq.:  -0.087) .. the roll-outs at 2-ply [world class] ran substantially longer and produced results that are still inconclusive regarding selecting a "best move" .. regardless, i think it has turned into an interesting problem and am eager to see what a more thourough analysis may yield

    1. Rollout          7/2 6/3                      Eq.:  -0.139
       0.431 0.000 0.000 - 0.569 0.052 0.022 CL  -0.139 CF  -0.139
      [0.003 0.000 0.000 - 0.003 0.001 0.001 CL   0.006 CF   0.006]
        Truncated cubeful rollout (depth 11) with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055060082 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]
~~~~~~~~~
    1. Rollout          7/2 6/3                      Eq.:  -0.142
       0.429 0.000 0.000 - 0.571 0.040 0.016 CL  -0.142 CF  -0.142
      [0.002 0.000 0.000 - 0.002 0.002 0.001 CL   0.004 CF   0.004]
        Truncated cubeful rollout (depth 11) with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055060082 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 2 0-ply moves and up to 3 more moves within equity 0.1
        keep the first 0 1-ply moves
        Cube: 2-ply cubeful prune [world class]

~~~~~~~~~~

while this move (13/8 7/4) was not one included as an optional answer, it produced a lower equity loss at 2-ply than did the 7/2 6/3 above and illustrates don's comment about "other" moves perhaps being better

    1. Rollout          13/8 7/4                     Eq.:  -0.136
       0.432 0.000 0.000 - 0.568 0.045 0.018 CL  -0.136 CF  -0.136
      [0.002 0.000 0.000 - 0.002 0.002 0.002 CL   0.004 CF   0.004]
        Truncated cubeful rollout (depth 11) with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 1055060082 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 2 0-ply moves and up to 3 more moves within equity 0.1
        keep the first 0 1-ply moves
        Cube: 2-ply cubeful prune [world class]

rather than randomly try others, i'll await someone describing how to use GNUbg rollouts to perform the in depth analysis this little problem apparently deserves (actually, i'm afraid being labelled a "facile" analyst :lol:)

for practical purposes and dare i say facile play, this position may be an example where analysis produces no clear readily seen tactical solution .. the strategic picture of how to approach the position however has two clear alternatives .. the approach of breaking the prime in an attempt to get two back and on the bar for a greater chance at winning is one i had not seen before .. thus, imo, it's a worthwhile little problem

Making one of the plays that forces the defender to hit with an immediate 6 is an imaginative play, but it isn't clearly correct. Rollouts of this position show that just clearing the bar point seems to do almost as well. Either of these strategies are however superior to just meekly bringing checkers home. Trapping Red off the anchor before the bearoff starts has to be good.
This the sort of position that you can learn a lot from if you roll it out yourself. Note that White has a difficult play here and will get many more before the end. Red's play is going to be simplicity itself. If Gnu tells you that White has a certain equity after any play here, you may assume that you are going to have to play brilliantly in order to achieve it. If you make Red hit with the next 6, I think that you are going to make your future play even more difficult, whether he hits or not. For example, if he doesn't roll a 6, are you going to leave the blot there next roll. Not sure? See what I mean? I vote for 7/4, 7/2 to keep it simple.

I tried dorpel's advice and played it couple of times to the end. The moves for white can truly be hard ones. For example after 12/9 7/2 and no six for red if now white rolls 4-1 it is correct to leave even more shots with 9/5 4/3. The same leaving blots thema continues also later unless white manages to close the board or can bear-off and there is no hits. Also after 7/4 7/2 gnu likes to leave blots in many positions later.