$$ \begin{aligned} \frac{2}{3}x+4 &= \frac{3}{2}(x-4)&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{2}{3}x+6\cdot4 &= 6 \cdot \frac{3}{2}(x-4)&& \text{cancel out the denominators} \\[1 em]4x+24 &= 9x-36&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]4x-9x &= -36-24&& \text{simplify left and right hand side} \\[1 em]-5x &= -60&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-60}{-5}&& \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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