$$ \begin{aligned} 3x+8 &= \frac{1}{3}x+12&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot3x+3\cdot8 &= 3 \cdot \frac{1}{3}x+3\cdot12&& \text{cancel out the denominators} \\[1 em]9x+24 &= x+36&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]9x-x &= 36-24&& \text{simplify left and right hand side} \\[1 em]8x &= 12&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{12}{8}&& \\[1 em]x &= \frac{3}{2}&& \\[1 em] \end{aligned} $$

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