I'm trying to figure out how to write a function (Let me explain it in an
example).

Lets say Column A is numbered from 1 - 20. In Column B there is a word that
could be one of four things (Apple, Bird, Cat, Dog). I am looking for a
function that will search for all Dogs and in another cell, write down the
number in Column A that corresponds with it.

Column A Column B
1 Cat
2 Dog
3 Apple
4 Dog
5 Bird

So in a Cell that i choose, it will list {2, 4}. Is this even possible to
do with a function?