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