$$ \begin{aligned} \frac{x}{8}+2 &= \frac{x}{4}-4&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8 \cdot \frac{x}{8}+8\cdot2 &= 8 \cdot \frac{x}{4}-8\cdot4&& \text{cancel out the denominators} \\[1 em]x+16 &= 2x-32&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 16 }$ to the right} \\[1 em]x-2x &= -32-16&& \text{simplify left and right hand side} \\[1 em]-x &= -48&& \text{switch signs on both sides} \\[1 em]x &= 48&& \\[1 em] \end{aligned} $$

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