Black to move
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(a) 1. …Qxe4 2.Qxe4 Nxh3+ 3.Kh1 ( or 3.Kg2 Rf2+ 4.Kh1 or Kxh3 Rh2# ) Rf1+ 4.Kg2 Rf2+ 5.Kh1 or Kxh3 Rh2#
(b) 1. …Qxe4 2.Qf1 ( 2.Qf2 Nxh3+ or 2.Qg3 Ne2+. In either case, Black wins. ) Nxh3+ 3.Qxh3 Qe1+ 4.Kg2 ( or 4.Qf1 Qxf1# ) Rf2#
(c) 1. …Qxe4 2.Ra8 ( threatening checkmate with 3.Rxf8# ) Qxa8 3.Qxa8 Rxa8 and Black will surely win.
1. ….. Qxe4 2. Qxe4 Nxh3+ 3. Kh1 (3. Kg2 Rf2+ 4. Kh1 [4. Kxh3 Rh2#] Rh2#) Rf1+ 5. Kg2 Rf2+ 6. Kh1 (6. Kxh3 Rh2#) Rh2#
i would like to rewrite part of my comment. That is as follows : (c) 1. …Qxe4 2.Ra8 ( threatening checkmate with 3.Rxf8# ) Qe1+ 3.Kh2 ( or 3.Qf1 Ne2+ 4.Kg2 or Kh1 Qxf1# ) Ne2+ 4.Kg2 Qg1#.