$$\frac { 2 y - 3 } { 2 } - \frac { y + 1 } { 3 } = \frac { 3 y - 8 } { 4 }$$
$y=2$
$$6\left(2y-3\right)-4\left(y+1\right)=3\left(3y-8\right)$$
$$12y-18-4\left(y+1\right)=3\left(3y-8\right)$$
$$12y-18-4y-4=3\left(3y-8\right)$$
$$8y-18-4=3\left(3y-8\right)$$
$$8y-22=3\left(3y-8\right)$$
$$8y-22=9y-24$$
$$8y-22-9y=-24$$
$$-y-22=-24$$
$$-y=-24+22$$
$$-y=-2$$
$$y=2$$
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