I can't seem to recall the name of this problem however, I do remember part of its description. Basically, there are three 3 rods similar to those of an abacus and on one of the rods there are 4 blocks ordered from largest to smallest from the bottom to the top. The problem is that you must shift the blocks on to another rod such that the blocks are ordered largest to smallest (from the bottom to the top) and in the process you are not allowed to put a larger block on top of a smaller block.
The closest picture I could find to this problem is
Note: This picture has more than 4 blocks and the blocks are all of the same size however, in the problem there are only 4 blocks and each of them are increasingly large (from the top to the bottom).
I hope this enough explanation for you to be able to pinpoint the name of this problem.
Thank you for your support.
It is called the Tower of Hanoi.