$$\frac{ 3y+1 }{ 16 } + \frac{ 2y-3 }{ 7 } = \frac{ y+3 }{ 8 } + \frac{ 3y-1 }{ 14 }$$
$y=5$
$$7\left(3y+1\right)+16\left(2y-3\right)=14\left(y+3\right)+8\left(3y-1\right)$$
$$21y+7+16\left(2y-3\right)=14\left(y+3\right)+8\left(3y-1\right)$$
$$21y+7+32y-48=14\left(y+3\right)+8\left(3y-1\right)$$
$$53y+7-48=14\left(y+3\right)+8\left(3y-1\right)$$
$$53y-41=14\left(y+3\right)+8\left(3y-1\right)$$
$$53y-41=14y+42+8\left(3y-1\right)$$
$$53y-41=14y+42+24y-8$$
$$53y-41=38y+42-8$$
$$53y-41=38y+34$$
$$53y-41-38y=34$$
$$15y-41=34$$
$$15y=34+41$$
$$15y=75$$
$$y=\frac{75}{15}$$
$$y=5$$
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