Why shouldn't the black king move to h7? If white plays ne6+, why shouldn't black play kh7?
1...Kh7 leads to 2. Qxh6+! Kxh6 3. Rh3+ with mate in 2. If 2...Kg8, Black is mated with 3. Qxg6 Kh8 4. Rh1 with mate in 2.