To simplify the expression \((6^2)^4\) using the Power Rule of Exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
In this case, we have:
\[ (6^2)^4 = 6^{2 \cdot 4} \]
Now, calculate the exponent:
\[ 2 \cdot 4 = 8 \]
So, we have:
\[ (6^2)^4 = 6^8 \]
Thus, the simplified expression is:
\[ \boxed{6^8} \]