Homomorphisms and Isomorphisms · Hard problem

A homomorphism $\varphi: \mathbb Z_{12} \to \mathbb Z_{18}$ is determined by $\varphi(1)$. How many homomorphisms $\varphi: \mathbb Z_{12} \to \mathbb Z_{18}$ send $1$ to an element of order exactly $3$ in $\mathbb Z_{18}$?