Which sentence shows the correct use of a common homophone?
the art teacher thought you’re drawing was exceptionally detailed.
some of the neighbors just saw you’re dog running down the street.
i think you left your biology notebook on the bleachers yesterday.
if you want to finish the assignment, your going to need another pen.

Let's go though all the sentences:
 
1)The art teacher thought you’re drawing was exceptionally detailed.
here it should be "your", not "you're" -it's possessive

2)Some of the neighbors just saw you’re dog running down the street.
here it's also possessive: your dog, not you're dog

3)I think you left your biology notebook on the bleachers yesterday.
-this is the correct sentence! it's a possessive form and it needs to be a possessive form

4) If you want to finish the assignment, your going to need another pen.
Here the possessive form is wrong! it should be "you're going"