After the rook moves to G5 why shouldn't the knight move to H6? In that way he will be protecting the knight piece.
Equalizing.
I agree with AnandPaxonet. The puzzle you have might be how your game went down, but Nh6 is definitely a better move than Nf6. ^.^
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This is from one of my games, and my first attempt at a puzzle, so all comments/suggestions are welcomed!