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So, i can play h7 x g6 or the other option is Qe3+

Qe3+ threatens nothing.

Ne1, Qc3
fxg8, Qe3+ (da!)

  1. Ne1! Qc3
  2. fxg6 Qe3+
  3. Kh1 and white wins.

Ne1! Qc3
fxg6 Qe3+
Kh1 Re8

That is pointless, you lost already a piece.
After Re8 I play Qxh7+ and then if Re7 Nc2.

Nf3.

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