If the parabola ${y^2} = 4\,\,ax$ passes through the point $\left( { - 3,2} \right),$ then the length of its latus rectum is-

$\begin{array}{l} y^{2}=4 a x \\ (-3,2) \rightarrow 4=4 \times a x-3 \\ \therefore a=-1 / 3 \end{array}$

$\therefore$ latus rectum $|4 a|=\frac{4}{3}$