Answer
$\dfrac{3}{5x}$
Work Step by Step
The given expression, $
\dfrac{2}{5x}\div\dfrac{4-18x}{6-27x}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2}{5x}\cdot\dfrac{6-27x}{4-18x}
\\\\=
\dfrac{2}{5x}\cdot\dfrac{3(2-9x)}{2(2-9x)}
\\\\=
\dfrac{\cancel{2}}{5x}\cdot\dfrac{3(\cancel{2-9x})}{\cancel{2}(\cancel{2-9x})}
\\\\=
\dfrac{3}{5x}
.\end{array}
