$$ \begin{aligned} \frac{6(x-4)}{2} &= \frac{3(x+6)}{11}&& \text{multiply ALL terms by } \color{blue}{ 22 }. \\[1 em]22 \cdot \frac{6(x-4)}{2} &= 22 \cdot \frac{3(x+6)}{11}&& \text{cancel out the denominators} \\[1 em]66x-264 &= 6x+36&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -264 }$ to the right} \\[1 em]66x-6x &= 36+264&& \text{simplify left and right hand side} \\[1 em]60x &= 300&& \text{ divide both sides by $ 60 $ } \\[1 em]x &= \frac{300}{60}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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