The amount of pizza she wants is:
[tex]\dfrac{1}{6}[/tex] of the pizza.
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:
[tex]\dfrac{1}{2}\times \dfrac{1}{3}=\dfrac{1}{6}[/tex]
This means that Becky wants 1/6 parts of the whole pizza.