The positive difference between two consecutive even perfect squares is $268$. Compute the larger of the two squares.

Note that 62^2 = 3828 and 64^2 = 4096 and 4096 - 3828 = 268, so the larger square is 4096.

Thanks for trying but the answer is 4624

The first Guest's mistake was in saying that 62² equals 3828.  It does not. 

Even without checking it, you can see at a glance that 62² will end with a 4.