Solution

The winning line is: 1. Rxg6+ fxg6 2. Qxg6+ Kh8 3. Nf6 Rh4 4. Nh5 Rxh5 5. Qxh5+ Kg7 6. Qh7+ Kf8 7. Qxe7+ Kg8 8. Bh7+ Kh8 9. Qf6+ Kxh7 10. Re7+ Bf7 11. Rxf7+ Kg8 12. Qg7#
White to play and win. But there is only one way
The winning line is: 1. Rxg6+ fxg6 2. Qxg6+ Kh8 3. Nf6 Rh4 4. Nh5 Rxh5 5. Qxh5+ Kg7 6. Qh7+ Kf8 7. Qxe7+ Kg8 8. Bh7+ Kh8 9. Qf6+ Kxh7 10. Re7+ Bf7 11. Rxf7+ Kg8 12. Qg7#