\[- \frac{54a^{6}b^{9}}{c^{12}} \cdot \left( - \frac{c^{20}}{12a^{4}b^{15}} \right) =\]
\[= \frac{54a^{6}b^{9}c^{20}}{12a^{4}b^{15}c^{12}} = \frac{9a^{2}c^{8}}{2b^{6}}.\]