If black refuses to take the R and goes to f8 something like this may happen. (not sure of best moves on either side)1.Rb6 Qf8 2.Qd4 Re8 3.Re6 Nxe6 4.fxe6 f6 5.Rxf6 Qd6 6.exd7 Qxd7 7.Qxe5 Kg8 8.Re6 Rxe6 9.dxe6 Qe7 10.Qb8+ Qf8 11.Qg3+ Kh8 12.e7 Qf7 13.e8=Q+ Qxe8 14.Qg7#
1. Rb6!!. Qxb6. 2. Qg3! Threatening mate at g7.
A- 1……Rg8. 2. Qxe5+. f6. 3. Nxf6. Rg7. 4. Qb8+!. Bc8. 5. Qxc8+. Qd8. 6. Qxd8+. Rg8. 7. Qxg8#
B- 1……Qh6. 2. Qxe5+. Kg8. 3. Nf6+!. Kf8. 4. Qd6+!. Kg7. 5. Rf4!!. Qxf4 ( hoping for 6. Qxf4. Kxf6). 6. Nh5+!. Kg8. (If Kh8?. 7. Qf6+. Kg8. 8. Qg7#!). 7. Nxf4.. And black is punctured!
1.Rb6
If black refuses to take the R and goes to f8 something like this may happen. (not sure of best moves on either side)1.Rb6 Qf8 2.Qd4 Re8 3.Re6 Nxe6 4.fxe6 f6 5.Rxf6 Qd6 6.exd7 Qxd7 7.Qxe5 Kg8 8.Re6 Rxe6 9.dxe6 Qe7 10.Qb8+ Qf8 11.Qg3+ Kh8 12.e7 Qf7 13.e8=Q+ Qxe8 14.Qg7#
1.Rb6 Qb8/Qc7 2.Qg5 Ne6 3.dxe6 Rg8 4.Qf6+ Rg7 5.Qxg7#