How to make a digital comparator with multiple inputs?
The starting point for a problem like this is to draw out a truth table of the logic that you intend to have the circuit synthesize. Your intention is still somewhat vague even after the comments. 

If we guess that the input pairs c:d and b:a are actually representing two 2-bit binary numbers then the following truth table shows the output for when c:d == b:a.



You can then add additional output columns to the table to represent the other outputs you may desire. 

This should get you started. I won't present the whole final solution because you learn little from that. The mechanics for reducing the table shown for one output can be done following one of a number of known procedures including Karnaugh Maps.