\[\frac{6^{12} \cdot \left( 6^{3} \right)^{5}}{\left( 6^{5} \right)^{4} \cdot 6^{4}} = \frac{6^{12} \cdot 6^{15}}{6^{20} \cdot 6^{4}} = \frac{6^{27}}{6^{24}} =\]
\[= 6^{3} = 216\]