Question: Solving (or attempting to solve!) a 4-electron problem is not twice as hard as solving a 2-electrons problem. Would you guess it to be more or less than twice as hard? Why?

A four-electron problem that involves only electrons and no nucleus would be more than twice as hard to solve as a two-electron problem" because there is an exact analytic solution for me two-electron problem, but not for the four-electron problem.

However, what the question is probably asking about is finding the wave functions and energies for an atom with two electrons and an atom with four electrons. The two-electron problem is a three-body problem (with the nucleus as the third body).

The four-electron problem would be less man two times as difficult as the two-electron problem. This is because neither problem can be solved in analytic form like the hydrogen atom, but many of the approximations used in the approximate solution of the two-electron problem, such as regarding each electron to move in an average field of the other charges, would apply also in some form to the four-electron problem.