As far as I can tell, that wouldn’t work. White king couldn’t make it there in time to prevent a black pawn from making it to the other side of the board and getting promoted, not if the black king also moved toward in to block. Once black king prevents white king from blocking the pawns, it’s just a matter of time.
It might be that the key here is to get a head start on blocking those pawns. The first move should be to move white king to the left, putting it in a position better suited to do that.
As far as I can tell, that wouldn’t work. White king couldn’t make it there in time to prevent a black pawn from making it to the other side of the board and getting promoted, not if the black king also moved toward in to block. Once black king prevents white king from blocking the pawns, it’s just a matter of time.
It might be that the key here is to get a head start on blocking those pawns. The first move should be to move white king to the left, putting it in a position better suited to do that.