As it says in the title, this is a homework question, so try not to give everything away. I'm just looking for a starting point. The question is stated as follows:
Let $R$ be a commutative, unital ring. Recall that $a\in R$ is a unit, if $a$ has a multiplicative inverse in $R$. Also, recall that for $b,c\in R$ we say $b$ divides $c$, if there exists some $d\in R$ such that $c=bd$.
Let $a$ be a unit. Prove that $b$ divides $c$, if and only if $ab$ divides $c$.