For the canonical map of f: Z-->Z6 (Z is integer and is Z6 is Integers with a little 6 below it)

Find the:

a.) Image of 6

So the answer is f(6)={...-12,-6,6,12,18...}

But i dont understand how this answer comes about.

&

b.) pre image of 3 (with a little bar on top).

so i assume we find a pre image of f(3)={...-9,-6,-3,3,6,9...} ? which i dont know why?

But i dont know how to find a pre image of this. I understand the concept of pre image but not with this.

There are other problems like this but i figure if someone can explain how the answers to these two come about i can figure out the rest and learn something.