$\frac{x +4}{5} - (x -4) = \frac{x}{3} - \frac{x -2}{2}$
$⇔ \frac{6.(x +4)}{30} - \frac{30.(x -4)}{30} = \frac{10x}{30} - \frac{15.(x -2)}{30}$
$⇔ 6.(x +4) -30(x -4) = 10x -15.(x -2)$
$⇔ 6x +24 -30x +120 = 10x -15x +30$
$⇔ -24x +144 = -5x +30$
$⇔ -24x +5x = 30 -144$
$⇔ -19x = -114$
$⇔ x = 6$
$Vậy$ $S =$ {$6$}