Step-by-step explanation
The four posters must be arranged in a row so we basically have a row with four different spots. Let's count the spots from left to right so that the first spot is where she will hang a poster is the one in the left. There are 4 possible choices for the first spot, let's assume that she decided to hang a certain poster and continue to the next spot. At this point she has already hang a poster so for the second spot we have 3 possible choices. Just like before we can assume that she hanged one of these three posters and then we continue to the third spot. By now she only has two posters left so there are 2 possible choices for this spot. Then for the final spot she'll only have 1 possible choice.
In order to find on how many ways can Ariana arrange the posters in the wall we just need to multiply the number of possible choices on each spot. Then the number we are looking for is given by:
Answer