Answer
$\dfrac{12}{5}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, the given expression, $
\dfrac{4x+8y}{3}\div \dfrac{5x+10y}{9}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4x+8y}{3}\cdot \dfrac{9}{5x+10y}
\\\\=
\dfrac{4(x+2y)}{3}\cdot \dfrac{3\cdot3}{5(x+2y)}
\\\\=
\dfrac{4(\cancel{x+2y})}{\cancel{3}}\cdot \dfrac{3\cdot\cancel{3}}{5(\cancel{x+2y})}
\\\\=
\dfrac{12}{5}
.\end{array}
