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

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