White to move and mate in two
The hints below could be of hep if you want to try to solve the Study; otherwise simply look at the solution published underneath the hints.
Black's King has no legal move, so every check is mate. Unfortunately there is no immediate mate (this is a "mate in two" study after all :) so we have to find a move that does not ruin our position to start with.
Not only Black's King has no move, but none of the other Black pieces has a reasonable move, so Black is in Zugzwang. White needs a "neutral" move which does not change anything and simply passes the move to Black.
Black's King has no move but White cannot mate in one: 1. Bf3+ Kxe6; 1. e4+ Kxd4; 1. Qf3+ Kd6; 1. Nc7+? Qxc7 would all still bring to mate, but certainly not in two! Black's other pieces have no move either: any Queen move allows Nc7 or Qe5; if Nxe6 or Bxe6 then Bf3 is mate, and if gxh5 then Bf3 is again mate, because the Rook defends the e6 pawn. So White has to find a neutral move, which passes the move to Black.
Note that all of White pieces are perfectly placed and any move from them would change things dramatically, basically making a mate in two impossible. The only White piece which can move without doing any damage to the position is the King, but the King has no less then eight legal moves, and of course only one of those move must be correct (because a Study can have one and only one solution). Let's check:
1. Kh3 Be6! (now Bf3 is not possible because the bishop is pinned to the King)
1. Kf3 Be6 (and Qf3 is not possible of course)
1. Kg3/h2 Bd6!
1. Kf2/g1 Bxd4! (as e4 is not impossible because the e-pawn is pinned to the King)
So the only waiting move for White is 1. Kh1!!, after which Black has no way to avoid the mate next move.