解：由$6x - 2y = 3$得$3x - y=\frac{3}{2}$ $③，$将$③$代入$(3x - y)(3x + 4y)=6$得$\frac{3}{2}(3x + 4y)=6，$$3x + 4y = 4$ $④。$$③×4 + ④$得：$4(3x - y)+3x + 4y = 4×\frac{3}{2}+4，$$12x - 4y+3x + 4y = 6 + 4，$$15x = 10，$解得$x=\frac{2}{3}。$把$x=\frac{2}{3}$代入$③$得：$3×\frac{2}{3}-y=\frac{3}{2}，$$2 - y=\frac{3}{2}，$解得$y=\frac{1}{2}。$所以方程组的解为$\begin{cases}x=\frac{2}{3} \\ y=\frac{1}{2}\end{cases}$
