1. The problem involves evaluating the factorial expression $4!$. 2. The factorial of a positive integer $n$, denoted $n!$, is the product of all positive integers from 1 to $n$. 3. The formula is: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 4. For $4!$, this means: $$4! = 4 \times 3 \times 2 \times 1$$ 5. Calculate step-by-step: $$4 \times 3 = 12$$ $$12 \times 2 = 24$$ $$24 \times 1 = 24$$ 6. Therefore, the value of $4!$ is $24$. 7. Factorials are used in permutations, combinations, and many areas of mathematics involving counting and probability.