Answer
$\dfrac{2}{9}$
Work Step by Step
The given expression, $
\dfrac{2k+8}{6}\div\dfrac{3k+12}{2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2k+8}{6}\cdot\dfrac{2}{3k+12}
\\\\=
\dfrac{2(k+4)}{6}\cdot\dfrac{2}{3(k+4)}
\\\\=
\dfrac{\cancel{2}(\cancel{k+4})}{\cancel{2}(3)}\cdot\dfrac{2}{3(\cancel{k+4})}
\\\\=
\dfrac{2}{9}
.\end{array}
