Direct Products and Finite Abelian Groups · Challenge problem

In $\mathbb Z_{12} \times \mathbb Z_4$, let $N = \langle(6,2)\rangle$ (order $2$, since $2\cdot(6,2)=(12,4)=(0,0)$). How many elements of the quotient $(\mathbb Z_{12}\times\mathbb Z_4)/N$ have order $4$?