The easiest solution is to assume that at the time both pumps started working on the basement, there were 12 units of water in the basement. This is the least common multiple of 4 and 3. Accordingly, the basement had 24 units of water in it when it was full.

Since the pump X evacuated 12 units of water in 4 hours, it must be pumping 3 units of water per hour. Together the pumps finished the rest of the job in 3 hours. That means that they must be pumping at 4 units per hour -- 3 units per hour from pump X and 1 unit per hour from pump Y.

Therefore, it would have taken the pump Y 24 hours to pump out the 24 units of water. This is answer choice E.