How to build a 3-bit comparator using a multiplexer?
Given 3 x 74LS153, consider using a 74LS153 (which is really a 2 x 4:1 multiplexers) to generate A > B and A &lt; B given A is a 1 bit value and B is a 1 bit value and that these bits form the least significant bit pair.  It can be inferred that if both A > B and A &lt; B are false then A = B.  Consider using the next 74LS153 for the next most significant bit pair.  However, for this and all other bit pairs, when A = B, pass the A > B &amp; A &lt; B outputs of the previous 74LS153.  We can repeat this (pattern) for as many bits pairs as needed.  The problem is constrained to 3 pairs. I will leave the exercise of wiring up to you to complete the problem.

Regardless if you are designing combinational logic or writing software.  Finding repeating patterns is usually the first step in simplifying the problem.