Bob and mark talk about their families. bob says he has three kids, the product of their age is 72. he gives another clue: the sum of the ages of his children. mark points out there is still not enough information to accurately guess. finally bob says, my youngest called justice. mark then correctly determine the ages of bobs children. what are the ages.

Bob says he has 3 kids, the product of their age is 72.
So the possible ages of Bob's kids can be taken from the factors of 72

72 = 2 * 2 * 2 * 3 * 3

Finally, bob says, my youngest child called justice.
So meaning, Bob has a youngest child. He didn't mention about a twin.

So the possible ages the following:
1, 2, 36 --> sum: 39
1, 4, 18 --> sum: 23
1, 8, 9 --> sum: 18

Once the sum of the ages will be revealed, then the possible ages are mentioned above.