$$ \begin{aligned} \frac{1}{2}x-10 &= \frac{1}{4}x+8&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{2}x-4\cdot10 &= 4 \cdot \frac{1}{4}x+4\cdot8&& \text{cancel out the denominators} \\[1 em]2x-40 &= x+32&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -40 }$ to the right} \\[1 em]2x-x &= 32+40&& \text{simplify left and right hand side} \\[1 em]x &= 72&& \\[1 em]x &= 72&& \\[1 em] \end{aligned} $$

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