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