Justin, thanks for posting your question.

You are supposed to prove the following:

Let $a,b,c\in \mathbb{N}$. Then $ac$ divides $bc$ if and only if $a$ divides $b$.

For the first half of your proof, you should assume that $ac$ divides $bc$. What does this tell us? (Appeal to the definition of "divides.") The next step involves doing some simplifying. Then argue that $a$ divides $b$.

For the second half of your proof, you should assume that $a$ divides $c$. What does this tell us? Now, can you obtain an equation involving $ac$ and $bc$? (You should essentially reverse your steps from the first half.) Argue that $ac$ divides $bc$.

I hope that helps.