Answer
$\log_6 2+\log_6 x-3\log y$
Work Step by Step
Using the properties of logarithms, then,
\begin{array}{l}
\log_6 \dfrac{2x}{y^3}
\\\\=
\log_6 2x-\log y^3
\\\\=
\log_6 2+\log_6 x-\log y^3
\\\\=
\log_6 2+\log_6 x-3\log y
.\end{array}