Quotient group always free over $\mathbb{Z}/m\mathbb{Z}$

Question

Im reading in some notes, that for any abelian group $G$ the quotient group $G/mG$ of $G$ is always free over $\mathbb{Z}/m\mathbb{Z}$. Isn't this false in general. We can take $G=\mathbb{Z}/6\mathbb{Z}$ and $m=4$. Then $G/mG$ is $\mathbb{Z}/2\mathbb{Z}$ and not free over $\mathbb{Z}/4\mathbb{Z}$. Or am i missing something?