$$ \begin{aligned} 4-\frac{1}{2}x &= 8+\frac{1}{2}x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot4-2 \cdot \frac{1}{2}x &= 2\cdot8+2 \cdot \frac{1}{2}x&& \text{cancel out the denominators} \\[1 em]8-x &= 16+x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 8 }$ to the right} \\[1 em]-x-x &= 16-8&& \text{simplify left and right hand side} \\[1 em]-2x &= 8&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{8}{2}&& \\[1 em]x &= -4&& \\[1 em] \end{aligned} $$

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