The task is: You have two letters A and B, how you can order it with repetition ?
I know the result is 2 x 2 but I have no idea what category is it. I've made some theory that it should be a permutation because n is not bigger than $p$, so I tried to solve it with the repetition permutation formula: $2! /( 1! 1!)$ (the formula says divide it by the factorial of numbers that shows how much time the characters are repeated. A and B repeated just once in the list so why not ? It is logical... But of course it gave me a different result.
I don't really know what is going on...
I think you managed to confuse yourself with the language: "how can you order A and B with repetition?"
On the one hand: when you say you want to 'order A and B', then it seems as if you already have 1 A and 1 B, i.e. you have a set of pre-existing objects ... and that would be about permutations: you arrange, but don't pick, since you already picked what you want to arrange.
On the other hand, once you throw in 'with repetition', you are suggesting that you no longer have a pre-existing set of objects that you merely want to rearrange (order), but rather you pick a first object that can be an A or B, and then a second that is an A or B .. that is, you seemed to use 'repetition' more like the concept of 'replacement' ... so now you pick and rearrange .. and so now it's about variations.