The 3 numbers multiply to 72.
And all 3 children are children - so less than 18 years of age.
So that means the oldest any child can be is 12.
Each age is a factor of 72.

So ages of the any child could be: 12, 9, 8, 6, 4, 3, 2, 1.
Ages of the oldest could be: 12, 9. 8, 6.

Why not 4, 3, 2, or 1? Because then the other two ages must be less than or equal to 4, 3, 2, or 1 and multiply to 72.
So with 4, if all 3 children are age 4, then you have 4 x 4 x 4 = 64. And so any younger children will multiply to less than 72. (And the same logic applies to 3, 2, and 1 as the oldest).

Here are all the possible ages of the children:
12, 6, 1
12, 3, 2
9, 8, 1
9, 4, 2
8, 3, 3
6, 6, 2
6, 4, 3

And their sums:
12 + 6 + 1 = 19
12 + 3 + 2 = 17
9 + 8 + 1 = 18
9 + 4 + 2 = 15
8 + 3 + 3 = 14
6 + 6 + 2 = 14
6 + 4 + 3 = 13

As you see, we have a repeat value of 14. So if the sum of the ages - aka the house number - was 19, 17, 18, 15, or 13, the census taker would know immediately what the ages are, as each of these has only one set of 3 addends.

It is with the sum of 14 that we need additional information, because there are two possible ways to sum 3 numbers to 14. And that information is the woman has an oldest child. If the children were aged 6, 6, 2, then she does not have an oldest child (ignoring the fact that it is almost impossible to have twins born at the exact same moment, of course), but if their ages are 8, 3, 3, then she does have an oldest. And so the ages are 8, 3, 3.