\[\frac{216a^{6}}{343b^{3}}\ :\frac{18a^{8}}{49b^{4}} \cdot \frac{7a^{3}}{4b^{2}} =\]
\[= \frac{216a^{6} \cdot 49b^{4} \cdot 7a^{3}}{343b^{3} \cdot 18a^{8} \cdot 4b^{2}} = \frac{3a}{b}.\]