$$ \begin{aligned} \frac{1}{3}(x+6) &= \frac{1}{4}x+8&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{1}{3}(x+6) &= 12 \cdot \frac{1}{4}x+12\cdot8&& \text{cancel out the denominators} \\[1 em]4x+24 &= 3x+96&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]4x-3x &= 96-24&& \text{simplify left and right hand side} \\[1 em]x &= 72&& \\[1 em]x &= 72&& \\[1 em] \end{aligned} $$

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