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Looks to me like the quarter-board puzzle 11 (as shown at http://www.ibiblio.org/twixtpuzzles/).
The suggested answer is 9.e5, and the main line of play is given as 10.d6 11.f3 12.f5 13.g4.
I think that the normal thing to try after 11.f3 is 12.g4. And I'm not so sure that it doesn't work. Certainly, there doesn't seem to be an easy way around. I may even need to apologize for posting here, since the linking rules are different here from the ones in the puzzle.
Is there a puzzle where the answer is to do something like g4? I can't think of one.
If 13.h5 14.h2, I think 15.g1 16.f5 17.f4 18.g2 19.e2 wins for white.
In puzzle 42, there is a peg at the h5-equivalent. It's an important pattern, because it is not unusual to see someone try to coign around a situation, like this: |1.i9 2.j6 3.g8 4.h5 5.f6 6.e4, and then 7.e5 8.d6 9.f3 10.g4 (the g4 peg you suggested) and then 11.h4 12.f5 13.g6 14.g7 or 11.g5 12.h6, and White is toast. But you need that extra peg in a good spot to make it work. (That was not a great example, because White should have ended it with 5.d5.)