Three (bad) things happened. 1) You weakened your kingside by playing g4. 2) Black castled O-O-O, to take advantage of number 1, while protecting his king behind the phalanx of (doubled) pawns. 3) The worst thing that happened was that 13. Nxg6 hxg6 opened up the h file for Black in front of a rook that had not moved. You should have moved the N back to f3 to keep a defender in place, and to keep the h file closed. On move 14, your best chance was the defensive Qf3, rather than the developing d4. You had a won game up to move 13, and a lost game after 14...Rxh3.
Tom Au
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