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(a) 1.Rxg6+ fxg6 2.Ne6+ Kf7 3.Nxd8+ Raxd8 4.Be6+ ＋－
(b) 1.Rxg6+ hxg6 2.Nh5+
(b1) 2. …gxh5 3.Qxh5 ( threatening checkmate with 4.Qh7# ) Re8 ( or 3. …Nh6 4.Qxh6+ Kg8 5.Qh7# ) 4.Qh7+ Kf8 5.Bh6+ Nxh6 6.Qxh6+ Kg8 7.Qh7+ Kf8 8.Qh8#
(b2) 2. …Kh6 3.Nf6++ Kg7 4.Qh7#
(b3) 2. …Kh7 3.Nf6++ Kg7 4.Qh7#
(b4) 2. …Kh8 3.Nf6+ Nh6 ( or 3. …Kg7 4.Qh7# ) 4.Qxh6#
(c) 1.Rxg6+ Kh8 2.Rxg8+ Rxg8 ( or 2. …Kxg8 3.Qxh7# ) 3.Qxh7#
P.S. There is another (a) variation. That’s as follows : 1.Rxg6+ fxg6 2.Ne6+ Kf7 3.Nxd8+ Raxd8 4.Qxh7+ Ke8 5.Qxg6+ Rf7 6.Qxg8+ Rf8 7.Qg6+ Rf7 8.Be6 Rd7 9.Qxf7+ ＋－.
1. Rxg6+
1…Kh8 2. Rxg8+ Rxg8 3. Qxh7#
1…hxg6 2. Nh5+ gxh5 [2…Kh8 3. Nf6+ Nh6 (3…Kg7 4. Qxh7#) 4. Qxh6#] 3. Rg1+ Bg5 [3…Kh8 4. Qxh5+ Nh6 5. Qxh6#] 4. Bxg5 Re8 [4…Qxg5 5. Rxg5+ Kh8 6. Qxh5+ Nh6 7. Qxh6#] 5. Bh6+ Kxh6 6. Qe3+ Qg5 7. Qxg5#
1…fxg6 2. Ne6+ Kh8 3. Bxg6 Rf7 4. Nxd8 Rxd8 5. Bxf7 +-
1. Bxg6 (threat Qxh7#) fxg6 2. Nh5+ Kh8 3. Rxg6 Rf7 (if hxg6 Nf7+ and Qh7#) 4. Rg7 RxR 5. NxR NxN 6. Rg1+ Kh8 7. Bh6 +-
Yes, this is also very strong, but White played 1.Bxg6 and then 2.Nh5.
Also possible, but White played 1.Bxg6 and 2.Nh5+ winning quickly.
On 1…fxg6 2.Ne6 wins. But if 1…hxg6 2.Nh5 wins.