1. The problem asks us to evaluate the permutation expression $4P4$. 2. The formula for permutations is: $$nPr = \frac{n!}{(n-r)!}$$ where $n$ is the total number of items, and $r$ is the number of items chosen. 3. For $4P4$, we have $n=4$ and $r=4$. 4. Substitute into the formula: $$4P4 = \frac{4!}{(4-4)!} = \frac{4!}{0!}$$ 5. Recall that $0! = 1$, so: $$4P4 = \frac{4!}{1} = 4!$$ 6. Calculate $4!$: $$4! = 4 \times 3 \times 2 \times 1 = 24$$ 7. Therefore, the value of $4P4$ is: $$4P4 = 24$$