The language was a bit confusing:
if Six different balls => Balls A, B, C, D, E, F
answer: 3 * 2 * 1 * 3 * 3* 3 = 162
If not then (balls are identical)
only three possible sets of numbers satisfy the condition
1 + 2 + 3 ( # of ways = 3! = 6)
1 + 1 + 4 ( # of ways = 3!/2 = 3)
2 + 2 + 2 ( # of ways = 1)
Total # of ways = 6 + 3 + 1 = 10 ways