\[\frac{6a - 6b}{c^{2}} \cdot \frac{4c^{6}}{a^{2} - b^{2}} =\]
\[= \frac{6(a - b) \cdot 4c^{6}}{c^{2}(a - b)(a + b)} = \frac{24c^{4}}{a + b}.\]