Answer:
The amount of pizza she wants is:
 
 of the pizza.
 of the pizza.
Explanation:
If there is 1/3 of a pizza left, and Becky only wants to eat 1/2 of it.
Then the amount of pizza she wants is:
 1/2 of the amount of the pizza left.
i.e. she wants:

This means that Becky wants 1/6 parts of the whole pizza.