find all homomorphism form Z6 to Z4?
Hint: Any homomorphism is completely determined on $\displaystyle [1]_6$ because $\displaystyle \left< [1]_6\right> = \mathbb{Z}_6$.
Now there are four possbilites:
$\displaystyle [1]_6\mapsto [0]_4$
$\displaystyle [1]_6\mapsto [1]_4$
$\displaystyle [1]_6\mapsto [2]_4$
$\displaystyle [1]_6\mapsto [3]_4$
Now check which ones are isomorphisms.