$$ \begin{aligned} \frac{1}{2}x+4 &= \frac{1}{3}(x+9)&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{1}{2}x+6\cdot4 &= 6 \cdot \frac{1}{3}(x+9)&& \text{cancel out the denominators} \\[1 em]3x+24 &= 2x+18&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]3x-2x &= 18-24&& \text{simplify left and right hand side} \\[1 em]x &= -6&& \\[1 em]x &= -6&& \\[1 em] \end{aligned} $$

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