Bob and mark talk about their families. bob says he has 3 kids, the product of their ages is 72. he gives another clue: the sum of the ages of his children. 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 bob's children. what are the ages?

To answer this, we try to list the possible ages of his children. Given above,

xyz=72

That first clue is not sufficient to produce a single solution, so Bob reveals the sum of their ages to Mark (sums sorted in ascending order): 
Age1        Age2      Age3              Sum
3                4              6                     13
2                6              6                     14
3                3              8                     14
2                4              9                     15
2                3              12                   17
1                8              9                     18
1                6              12                   19
2                2              18                   22
1                4              18                   23
1                3              24                   28
1                2              36                   39
1                1              72                   74

Mark says that there is still insufficient information, there must be duplicate sets of ages that produce a single product.  Here are the two:    
Age1        Age2      Age3              Sum
2                6              6                      14
3                3              8                      14

I think the correct answer are 2, 6, 6.