$$ \begin{aligned} \frac{x}{4}-3 &= \frac{x}{2}+3&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{x}{4}-4\cdot3 &= 4 \cdot \frac{x}{2}+4\cdot3&& \text{cancel out the denominators} \\[1 em]x-12 &= 2x+12&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]x-2x &= 12+12&& \text{simplify left and right hand side} \\[1 em]-x &= 24&& \text{switch signs on both sides} \\[1 em]x &= -24&& \\[1 em] \end{aligned} $$

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