nxh6 f7+ wins the queen back. and draws/wins for black
3- nxh6 f2+
4-Kf1 BxQ
5- NxB Bh2
6 Nf2++
Wabal your line gives mate in 6
1.Nf5+ Kh3 takes longer than 9.
That's the issue.
1. Nf5+ Kg2
2. Qg4+ Kh1
3. Nxh6 Kh2
4. Qg5 Kh1
5. Ng4 f2+
6. Nxf2+ Bxf2+
7. Kxf2 Bg4
8. Qh6+ Bh5
9. Qxh5#