To simplify the expression \(12^{12} \cdot 12^{-4}\), we can use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).
Applying this property, we have:
\[ 12^{12} \cdot 12^{-4} = 12^{12 + (-4)} = 12^{12 - 4} = 12^8 \]
Therefore, the simplified expression is:
\[ \boxed{12^8} \]