solve for t

$6t-\frac{2}{3}+\frac{t}{5}=\frac{8+\left(2-t\right)}{3}$

$6t\cdot \:15-\frac{2}{3}\cdot \:15+\frac{t}{5}\cdot \:15=\frac{8+2-t}{3}\cdot \:15$

$93t-10=5\left(-t+10\right)$

$93t-10=-5t+50$

$93t-10+10=-5t+50+10$

$93t=-5t+60$

$93t+5t=-5t+60+5t$

$98t=60$

$\frac{98t}{98}=\frac{60}{98}$

$t=\frac{30}{49}$