Black is in check, so Black is forced to deal with that first.
Black can't move out of check and can't take the checking piece so their only option is to block it. If Black blocks it with the Queen (Qc6) then White can take their knight which ends the immediate checkmate threat and leaves White up on material.
If Black blocks it with the rook (Rc6) then White still has to deal with the checkmate threats by Qb2 and Qc2. It seems to me that all White's options from this point result in a loss of material for White.
If (after Black plays Rc6) White use their rook or queen to check Black on their back rank then Black just captures the attacker with their rook. This leaves Black up on material and does nothing about the checkmate threat.
If White captures Black's rook with their queen (Qxc6+) then Black captures their queen with theirs (Qxc6). White gave up their queen in exchange for Black's rook.
Rc4 by White blocks the threat of mate by Qc2 but does nothing about the threat of mate by Qb2, so that doesn't help.
Nc4 by White mitigates the immediate threat of mate, but Black can capture their rook with their knight (Nxb4) reinstating the threat of a mate by Qc2. To stop that threat White pretty much has to capture Black's knight with their pawn (axb4).