It's White's turn. How many total possibilities are there to win the game with the minimum moves?
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Observe that the possible options for the king are to move to either d8 and f8 or by castling to the king's side. Because the king can't castle when checked, the final step is to promote the pawn to the piece, where the king is in check. In that case, it is impossible for the king to move to the safe position.
Since rook and queen both share the role in moving horizontally along the same rank, there are 2 total possibilities to win the game.
For more information of why castling out of check is not allowed, see the references: [1] , [2]