Alright! In order to solve this you have to work backwards. So, you know her end total is 36. And to get to that she bought 16 books. So:
36 - 16 = 20.
So, after she sold half her books she had 20. To find how many she started with you do the opposite of dividing by 2, multiplying by 2. So:
20 x 2 = 40.
She started with 40 books.