$\frac{x}{3}$= $\frac{y}{4}$ <-> x=$\frac{3y}{4}$
$\frac{y}{5}$= $\frac{z}{6}$ <-> z=$\frac{6y}{5}$
M=$\frac{2x+3y+4z}{3x+4y+5z}$= $\frac{2.\frac{3y}{4}+3y+4.\frac{6y}{5}}{3.\frac{3y}{4}+4y+5.\frac{6y}{5}}$ =$\frac{\frac{93y}{10}}{\frac{49y}{4}}$ = $\frac{186}{245}$