$$ \begin{aligned} \frac{2}{3}(x-3) &= \frac{1}{2}(x+12)&& \text{simplify left and right hand side} \\[1 em]\frac{2x-6}{3} &= \frac{x+12}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{2x-6}{3} &= 6 \cdot \frac{x+12}{2}&& \text{cancel out the denominators} \\[1 em]4x-12 &= 3x+36&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]4x-3x &= 36+12&& \text{simplify left and right hand side} \\[1 em]x &= 48&& \\[1 em]x &= 48&& \\[1 em] \end{aligned} $$

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