$$ \begin{aligned} x-6 &= \frac{1}{2}x+4&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x-2\cdot6 &= 2 \cdot \frac{1}{2}x+2\cdot4&& \text{cancel out the denominators} \\[1 em]2x-12 &= x+8&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]2x-x &= 8+12&& \text{simplify left and right hand side} \\[1 em]x &= 20&& \\[1 em]x &= 20&& \\[1 em] \end{aligned} $$

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