$$t-3+2(t+3) = 8-\frac{t}{3}-2$$

$$ \begin{aligned} t-3+2(t+3) &= 8-\frac{t}{3}-2&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3t-3\cdot3+3\cdot2(t+3) &= 3\cdot8-3 \cdot \frac{t}{3}-3\cdot2&& \text{cancel out the denominators} \\[1 em]3t-9+6t+18 &= 24-t-6&& \text{simplify left and right hand side} \\[1 em]9t+9 &= -t+18&& \text{move the $ \color{blue}{ -t } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]9t+t &= 18-9&& \text{simplify left and right hand side} \\[1 em]10t &= 9&& \text{ divide both sides by $ 10 $ } \\[1 em]t &= \frac{9}{10}&& \\[1 em] \end{aligned} $$

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