Final answer:
The number of different arrangements of Anita's books on her top and bottom shelves is 12.
Step-by-step explanation:
The number of different arrangements of Anita's books on her top and bottom shelves can be found using the concept of permutations. Since Anita has 4 different books and wants to place one on the top shelf and one on the bottom shelf, we need to find the number of permutations of 2 books taken from a total of 4 books. This can be calculated using the formula for permutations:
nPr = n! / (n - r)!
Substituting the values into the formula, we have:
4P2 = 4! / (4 - 2)! = 4! / 2! = 4 x 3 = 12 different arrangements