Three Daughters/Solution

Solution
The ages of the neighbour's three daughters are $9$, $2$ and $2$.

Proof
There are $8$ ways of selecting $3$ positive integers whose product is $36$:

Indeed, it is not possible to know what the ages are from just knowing the product of their ages.

Now we learn that the sum of their ages equals the house number at which they live.

Let us investigate what those house numbers could be, by examining the $8$ possibilities above:

Having looked at the house number, I still could not tell the ages of his daughters.

For all the sums except for $13$, those sums are the only way you can make that number from $3$ positive integers whose product is $36$

So the house number must be $13$.

Finally, I was told some information about the oldest daughter.

If the ages were $1$, $6$ and $6$, technically speaking there is no "oldest" daughter, as the $6$-year-olds are twins.

So for there to be an "oldest daughter", ages must be $2$, $2$ and $9$.

Quibbles
The assumption is that as they are both $6$ years old, the daughters of the $1$, $6$, $6$ family are twins.

However, by the convention that describing a child's age as $6$ means they can be anywhere between $6$ and $7$, it is possible that their ages are just-$6$ and nearly-$7$, and that the mother (poor woman) fell pregnant less than $3$ months after giving birth, or that the second child was severely premature.

Hence one of the $6$-year-olds could easily be referred to as the "oldest daughter".

Besides, it is of course quite possible for the neighbour to refer to the "older twin" as the "oldest daughter".