\[\frac{64^{2} \cdot 4^{7}}{16^{6}} = \frac{\left( 4^{3} \right)^{2} \cdot 4^{7}}{\left( 4^{2} \right)^{6}} = \frac{4^{6} \cdot 4^{7}}{4^{12}} = \frac{4^{13}}{4^{12}} = 4\]