{ 2, 2, 9}

If you list out the trio of factors that multiply to 36 and their sums, you get :

• 1 1 36 = 38
• 1 2 18 = 21
• 1 3 12 = 16
• 1 4 9 = 14
• 6 6 1 = 13
• 2 2 9 = 13
• 2 3 6 = 11
• 3 3 4 = 10

Since the number on the house next door is not enough information there must be more than 1 factor trio that sums up to it, leaving two possibilities: { 6, 6, 1} , {2, 2, 9} . When she says her 'oldest' you know it can not be {6,6,1} since she would have two 'older' sons not an 'oldest'.