$$ \begin{aligned} \frac{1}{2}(3x+4) &= \frac{2}{3}(x-4)&& \text{simplify left and right hand side} \\[1 em]\frac{3x+4}{2} &= \frac{2x-8}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{3x+4}{2} &= 6 \cdot \frac{2x-8}{3}&& \text{cancel out the denominators} \\[1 em]9x+12 &= 4x-16&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]9x-4x &= -16-12&& \text{simplify left and right hand side} \\[1 em]5x &= -28&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{28}{5}&& \\[1 em] \end{aligned} $$

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