$\left\{\begin{array}{l} mx-y=2m\\ 4x-my=m+6\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} 4mx-4y=8m\\ 4mx-m^2y=m^2+6m\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} (m^2-4)y=-m^2+2m\\ 4mx-m^2y=m^2+6m\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} (m-2)(m+2)y=-m(m-2)\\ x=\dfrac{my+m+6}{4}\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l}y=\dfrac{-m}{m+2}\\ x=\dfrac{2m+3}{m+2}\end{array} \right.\\ a)m=3 \Rightarrow \left\{\begin{array}{l}y=\dfrac{-3}{5}\\ x=\dfrac{9}{5}\end{array} \right.\\ b)3x+y=\dfrac{4}{3}\\ \Leftrightarrow 3\dfrac{2m+3}{m+2}-\dfrac{m}{m+2}=\dfrac{4}{3}\\ \Leftrightarrow \dfrac{5m+9}{m+2}=\dfrac{4}{3}\\ m=\dfrac{-19}{11}$
