How many number of group homomorphisms are there from $S_3$ to $A_3$ ??
In case of $Z_m$ to $Z_n$, I can map 1 to an element whose order divides order of both $Z_m$ and $Z_n$ (m and n).
What method should be applied to non abelian groups??
$S_3$ is of order 6 , $A_3$ is of order 3 Identity should be mapped to identity. And how can we conclude about mapping of other elements in $S_3$ to $A_3$..