Let $f: (\mathbb{Z}\_{24}, +) \rightarrow (\mathbb{Z}\_{36}, +)$
be a group homomorphism. If the image of $f$ contains exactly $2$ elements, how many elements are there in the kernel of $f$?

**What I know:**

Let $f : G \to H$ be a group homomorphism between two finite groups. Then we
have $$|G| = |\ker(f )| \times |{\rm im}(f )|$$
$$|G|= |\ker(f )| \times 2$$

However I don't know how to work out $|G|$ for my question.