Combinational circuit to check if two four bit numbers are equal
4 x Xor gate... and 4 input nor gate

Xor each pair of inputs then use a 4 input nor gate...

Xor gate gives 0 when both inputs are the same.

a 4 input nor gate gives a logic 1 if all inputs are 0, and 0 if any input is 1.

or

Not((X1 XOR Y1) OR (X2 XOR Y2) OR (X3 XOR Y3) OR (X4 XOR Y4))