$$ \begin{aligned} \frac{1}{2}(x+5) &= \frac{1}{3}(2x-4)+8&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{1}{2}(x+5) &= 6 \cdot \frac{1}{3}(2x-4)+6\cdot8&& \text{cancel out the denominators} \\[1 em]3x+15 &= 4x-8+48&& \text{simplify right side} \\[1 em]3x+15 &= 4x+40&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 15 }$ to the right} \\[1 em]3x-4x &= 40-15&& \text{simplify left and right hand side} \\[1 em]-x &= 25&& \text{switch signs on both sides} \\[1 em]x &= -25&& \\[1 em] \end{aligned} $$

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