$$\frac{ 3y-2 }{ 4 } = \frac{ 2x+8 }{ 6 }$$
$x=\frac{9y}{4}-\frac{11}{2}$
$$3\left(3y-2\right)=2\left(2x+8\right)$$
$$9y-6=2\left(2x+8\right)$$
$$9y-6=4x+16$$
$$4x+16=9y-6$$
$$4x=9y-6-16$$
$$4x=9y-22$$
$$\frac{4x}{4}=\frac{9y-22}{4}$$
$$x=\frac{9y-22}{4}$$
$$x=\frac{9y}{4}-\frac{11}{2}$$
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$y=\frac{4x+22}{9}$
$$9y=4x+16+6$$
$$9y=4x+22$$
$$\frac{9y}{9}=\frac{4x+22}{9}$$
$$y=\frac{4x+22}{9}$$
