$$\frac{2y-1}{3}-\frac{3y+1}{4}=y-6$$
$y=5$
$$4\left(2y-1\right)-3\left(3y+1\right)=12y-72$$
$$8y-4-3\left(3y+1\right)=12y-72$$
$$8y-4-9y-3=12y-72$$
$$-y-4-3=12y-72$$
$$-y-7=12y-72$$
$$-y-7-12y=-72$$
$$-13y-7=-72$$
$$-13y=-72+7$$
$$-13y=-65$$
$$y=\frac{-65}{-13}$$
$$y=5$$
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