$$ \begin{aligned} \frac{x}{4} &= 2+\frac{x-3}{3}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x}{4} &= 12\cdot2+12 \cdot \frac{x-3}{3}&& \text{cancel out the denominators} \\[1 em]3x &= 24+4x-12&& \text{simplify right side} \\[1 em]3x &= 4x+12&& \text{move the $ \color{blue}{ 4x } $ to the left side} \\[1 em]3x-4x &= 12&& \text{simplify left side} \\[1 em]-x &= 12&& \text{switch signs on both sides} \\[1 em]x &= -12&& \\[1 em] \end{aligned} $$

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