jmc

Solving $4x=3y$ for $x$ gives $x=\frac{3}{4}y$. Substituting this into the desired expression gives $$\begin{array}{rl}\frac{2x+y}{3x-2y}& =\frac{2\left(\frac{3}{4}\right)y+y}{3\left(\frac{3}{4}y\right)-2y}\\ & =\frac{\frac{3}{2}y+y}{\frac{9}{4}y-2y}=\frac{\frac{5}{2}y}{\frac{y}{4}}\\ & =\frac{5}{2}\cdot 4=\boxed{10}.\end{array}$$