$$\frac { 3 x - 2 } { 4 } - \frac { 2 x + 3 } { 3 } = \frac { 2 } { 3 } - x$$
$x=2$
$$3\left(3x-2\right)-4\left(2x+3\right)=8-12x$$
$$9x-6-4\left(2x+3\right)=8-12x$$
$$9x-6-8x-12=8-12x$$
$$x-6-12=8-12x$$
$$x-18=8-12x$$
$$x-18+12x=8$$
$$13x-18=8$$
$$13x=8+18$$
$$13x=26$$
$$x=\frac{26}{13}$$
$$x=2$$
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