[tex]Domain:v\neq0\\\\\dfrac{2}{v}+\dfrac{2}{3}=\dfrac{v-6}{3v}\\\\\dfrac{2\cdot3}{v\cdot3}+\dfrac{2\cdot v}{3\cdot v}=\dfrac{v-6}{3v}\\\\\dfrac{6}{3v}+\dfrac{2v}{3v}=\dfrac{v-6}{3v}\\\\\dfrac{6+2v}{3v}=\dfrac{v-6}{3v}\iff6+2v=v-6\qquad\text{subtract 6 from both sides}\\\\2v=v-12\qquad\text{subtract v from both sides}\\\\\boxed{v=-12}\to\boxed{A.}[/tex]
