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RxR threatening Nx e7 fork
I guess Qxp+ refutes that one
Rg6, obviously
Rg6 Pxg6
Pxg6 Rxg6
Pxg6 Kxg6
Ne7 black queen is forked game over
Rg6 forces the exchanges or else its Qxh6 mate. after the dust clears white has an easy fork.
wolverine
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Yes, white can save the game.
1. Rg6 [threatens Qh6#] fxg6 [or Rxg6 with same result]
2. hxg6+ Rxg6 [forced]
3. fxg6+ Kxg6
4. Qg2+ Kh5 [if Kf7, then Qg7+ and Qe7#]
5. Nf4#
Alternatively, black could try Kg8 at move 3, but white responds with Qxh6 leaving black no defense against Qg7#.
Rg6 Pxg6
Pxg6 Rxg6
Pxg6 Kxg6
Qg2 Kf7
Qf7+ Ke8
Qe7 mate
heres another way the mate could have happened
wolverine
shouldnt the question be can black save the game rg6 black has no defence against the upcoming knight fork and after the queen is out bishop on f6 and white queen can easily mate the black king for instance rg6 fg6 hg6 rg6 fg6 kg6 (exposes the king) ne7 kf6 nc6 rc8 qh6+ and the king hunt begins black is down materially as well as positionally his materials are not coordinating well enough. other variations begining with kg8 instead of kxg6 loses even more material