jmc

A constant term occurs when three of the terms in the product contribute $6x$ and other three contribute $\frac{1}{3x}$. Using the Binomial Theorem, we know that the constant term is $$\left(\genfrac{}{}{0ex}{}{6}{3}\right)(6x{)}^3{\left(\frac{1}{3x}\right)}^3=(20)(2{)}^3=(20)(8)=\boxed{160}.$$