1. The problem is to understand why $4 \times 3 \times 2 \times 1 = 24$. 2. This expression is a product of consecutive integers starting from 4 down to 1, which is called the factorial of 4, written as $4!$. 3. The factorial of a positive integer $n$ is defined as the product of all positive integers from $n$ down to 1: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 4. Applying this to $4!$, we multiply: $$4 \times 3 = 12$$ $$12 \times 2 = 24$$ $$24 \times 1 = 24$$ 5. Therefore, $4! = 24$ because multiplying these numbers step-by-step results in 24. 6. This is a fundamental concept in combinatorics and algebra used to count permutations and arrangements.