We need to simplify the expression $\frac{4!4!}{2!2!2!2!}$.

1. Problem Description

We need to simplify the expression $\frac{4!4!}{2!2!2!2!}$.

2. Solution Steps

First, recall the definition of a factorial: $n! = n \times (n-1) \times (n-2) \times ... \times 2 \times 1$.

Then, we evaluate the factorials in the expression.

$4! = 4 \times 3 \times 2 \times 1 = 24$

$2! = 2 \times 1 = 2$

Now substitute these values into the expression:

$\frac{4!4!}{2!2!2!2!} = \frac{24 \times 24}{2 \times 2 \times 2 \times 2} = \frac{576}{16}$

Finally, we divide 576 by 16:

$\frac{576}{16} = 36$

3. Final Answer

36