$$ \begin{aligned} \frac{3}{4}(2x-16) &= \frac{1}{3}(x+6)&& \text{simplify left and right hand side} \\[1 em]\frac{6x-48}{4} &= \frac{x+6}{3}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{6x-48}{4} &= 12 \cdot \frac{x+6}{3}&& \text{cancel out the denominators} \\[1 em]18x-144 &= 4x+24&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -144 }$ to the right} \\[1 em]18x-4x &= 24+144&& \text{simplify left and right hand side} \\[1 em]14x &= 168&& \text{ divide both sides by $ 14 $ } \\[1 em]x &= \frac{168}{14}&& \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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