Answer
$\dfrac{24}{7}$
Work Step by Step
$\sin{A} = - \dfrac{3}{5}$
$\cos{A} = -\sqrt{1-\left(\dfrac{-3}{5}\right)^2} = -\dfrac{4}{5}$
$\tan{A} = \dfrac{\sin{A}}{\cos{A}}= \dfrac{3}{4}$
$\tan{2A} = \dfrac{2 \tan{A}}{1- \tan^2 {A}}$
$\tan{2A} = \dfrac{2 \times \dfrac{3}{4}}{1-\left (\dfrac{3}{4}\right)^2} = \dfrac{24}{7}$
