\[\frac{a + 6b}{6ab} \cdot \frac{18a^{2}b^{3}}{a^{2} + 12ab + 36b^{2}} =\]
\[= \frac{(a + 6b) \cdot 18a^{2}b^{3}}{6ab \cdot (a + 6b)^{2}} = \frac{3ab^{2}}{a + 6b}.\]