$$ \begin{aligned} 2 \cdot \frac{x+4}{3}-8 &= 32&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot2 \cdot \frac{x+4}{3}-3\cdot8 &= 3\cdot32&& \text{cancel out the denominators} \\[1 em]2x+8-24 &= 96&& \text{simplify left side} \\[1 em]2x-16 &= 96&& \text{ move -16 to the right } \\[1 em]2x &= 96+16&& \\[1 em]2x &= 112&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{112}{2}&& \\[1 em]x &= 56&& \\[1 em] \end{aligned} $$

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