Answer: Your answer is completely correct. It is just that when answering the question, you should assume that the 48 lb child is on the left, and the 72 lb child is on the right. Usually, I always assume that the first mentioned item is the left most one.
Explanation:
This is how I will set up the problem: M1 = 48 lbs, M2 = 72 lbs, L = 10 ft
Since (M1 * 0 + M2 * 10)/(M1+M2) = equilibrium, we can use this equation to find the solution:
0 + 720 / (48+72) = 6 feet