Bob and mark talk about their families. bob says he has 3 kids, the product of their ages is 72. mark points out that there is still not enough information to accurately guess. finally, bob says, "my youngest child called justice." mark can then correctly determine the ages of bobs children. what are the ages?

Given:
3 kids
72 is the product of their ages.
There is a youngest child.

This means that all three are of different ages. We need to factor 72 into 3 integers.
Let us use prime factorization:

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
  9 ÷ 3 = 3

Prime factors are: 2 x 2 x 2 x 3 x 3    OR 2³ x 3²

3 ages.

eldest      = 3³ = 9
middle     = 2² = 4
youngest  = 2¹ = 2

2 x 4 = 8
8 x 9 = 72