Got this wrong, but can't understand the reasoning behind the correct move, any help appreciated.

You're going to hit with 13/9*. That leaves you with five possible threes, and every one makes your position worse. So now you have to find the least-bad play of a 3, and we typically don't do well with those because it's not a natural way of thinking. So let's start to eliminate possibilities by elimination.

First up: 8/5 and 6/3. Slotting when your opponent is on the bar is very unusual and generally happens only in back games or when the other plays are disasters. That's not the case here, so out they go.

Next: 21/18. This checker is better off where he is, and going to the 18 brings him under the big gun of White's midpoint for no gain.

Now we're down to the building 13/10 and the stacking 9/6. There are two problems with the building play: too many blots and we've stripped our midpoint, which is more costly than you might think this early in the game.

Now we get to 9/6. This leaves a spare on the midpoint, our back checkers where they belong, and only two blots. That's a lot of assets (or actually non-liabilities). The only problem with the play is the sixth checker on the 6-point. That's a liability, but the sum of the liabilities on each of the other plays is greater.

So I vote for 13/9*/6. (I was assisted by the fact that I just finished writing a chapter on stacking in my new book, and this position clearly fit the criteria.)

Thanks Bill, you are spot on as usual. I was put off the move by the enormous stack I would have ended up with on the 6 point, and opted for 21/18, which if I remember correctly is about a 0.15 blunder. 13/10 is the second best option, at 0.08