To simplify the expression \( 4^2 \cdot 4^2 \), we can use the property of exponents which states that \( a^m \cdot a^n = a^{m+n} \).
In this case, we have:
\[ 4^2 \cdot 4^2 = 4^{2+2} = 4^4 \]
Now we need to evaluate \( 4^4 \):
\[ 4^4 = (4^2)^2 = 16^2 = 256 \]
Therefore, the answer is:
\[ \boxed{256} \]