\[\frac{9a + 9b}{c^{6}} \cdot \frac{3c^{12}}{a^{2} - b^{2}} = \frac{9(a + b) \cdot 3c^{12}}{c^{6}(a - b)(a + b)} =\]
\[= \frac{27c^{6}}{a - b}\]