Two positive point charges are held in place, 0.92 m apart. They are then moved so that their electric potential energy doubles. What is the new separation between the charges?

0.46 m

The electric potential energy of the system is given by

U = k*q1*q2/r

k, q1 and q2 are fixed, so we can only change r, and as U is inversely proportional to r we need to halve r to double U.