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To attack unprotected Q + something else unprotected with a rook move looks reasonable:
1. Rh4!
Black Q can’t protect Rh8, or give check, but white can take Rh8 with check, so goodbye to that rook.
1. … Qxe3 (only try)
2. Rxh8+ Rc8 (trying to regain R, or keeping Q a move longer)
3. Rxc8 Bxc8/Kxc8
4. fxe3
Black’s queen is undefended, so white just needs to play Rh4 in this position.
R-h4 wins – both the rook and queen are attacked and neither is defended
e.g.,
… Qxe3
RxR+ wins a rook outright
Rh4