simple. There are three kids, their ages multiplied are 36 and they add up to some other number. Here are the options (multiplied) [added together]:
1, 1, 36, (36), [38]
1, 2, 18, (36), [21]
1, 3, 12, (36), [16]
1, 4, 9, (36), [14]
1, 6, 6, (36), [13]
2, 2, 9, (36), [13]
2, 3, 6, (36), [11]
3, 3, 4, (36), [10]
Then bob checks the house number and needs more information, which means that the bolded are only two options here, since they add up to the same number. If the neighbour's number was any of the others, Bob would have called the ages immediately.
Now, since Alice says that her oldest child (singular) plays the piano, then the answer is 2, 2, and 9. Not that six year olds can't play the piano, but as twins, it's a fair assumption that they would have played together.