It is white's move, but he must not checkmate... pretty straight forward, no?
No Mate
Rc6. Then the Black Rb7 is unpinned from its king and can capture the h7 bishop.
Ah!
1. Rc6+
It is not mate because White breaks his own pin on the b7 Rook, allowing it to capture the h7 Bishop that is checking the King.
Huh? I'm really lost... what does that have to do with anything?
Now I'm lost.... Rc6 isn't mate
Rc6. Then the Black Rb7 is unpinned from its king and can capture the h7 bishop.
Rc6 is the correct solution. This leaves black with only 1 move to prevent checkmate, which is to take the bishop on h7 which is providing the check. Also the Rc6 blocks the Ba8 from checking the king, which it would do because of the rook on b7... Here it is in an easy viewer
if the goal is
for white to move and not be in mate,
why not
1.Kf8...
1.Kf7...
neither results in mate...
White to Move and NOT Checkmate.