It is a review problem for abstract algebra, and I'm having trouble figuring it out.
Ring $R=\mathbb Z_4\times\mathbb Z_6$, which is a commutative ring with unity $(1,1)$. Find the units in this ring.
I know how to find units when $R=Z_4$ and $R=Z_6$ separately, but I don't know when it comes to $R=Z_4$ x $Z_6$. Should I list all the elements in $R$ first?