$$ \begin{aligned} \frac{x}{3} &= \frac{x}{2}-2&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x}{3} &= 6 \cdot \frac{x}{2}-6\cdot2&& \text{cancel out the denominators} \\[1 em]2x &= 3x-12&& \text{move the $ \color{blue}{ 3x } $ to the left side} \\[1 em]2x-3x &= -12&& \text{simplify left side} \\[1 em]-x &= -12&& \text{switch signs on both sides} \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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