To simplify the expression \((12 \cdot 12 \cdot 12) \cdot (12 \cdot 12 \cdot 12)\) using the Power Rule of Exponents, we can first rewrite the expression:
Each group of \(12\) has three factors, so we can express it in exponential form:
\[ (12^3) \cdot (12^3) \]
Using the Power Rule of Exponents, which states that \(a^m \cdot a^n = a^{m+n}\), we can simplify this further:
\[ 12^3 \cdot 12^3 = 12^{3+3} = 12^6 \]
Thus, the simplified equivalent expression is:
\[ \boxed{12^6} \]