Answer
$\dfrac{1}{2pq}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(3pq)q^2}{6p^2q^4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\cancel{3}pq^{1+2}}{\cancel{3}(2)p^2q^4}
\\\\=
\dfrac{pq^{3}}{2p^2q^4}
\\\\=
\dfrac{p^{1-2}q^{3-4}}{2}
\\\\=
\dfrac{p^{-1}q^{-1}}{2}
\\\\=
\dfrac{1}{2p^1q^1}
\\\\=
\dfrac{1}{2pq}
.\end{array}