$$ \begin{aligned} \frac{4}{5}(15x+20)-7x &= \frac{5}{6}(12x-24)+6&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{4}{5}(15x+20)-30\cdot7x &= 30 \cdot \frac{5}{6}(12x-24)+30\cdot6&& \text{cancel out the denominators} \\[1 em]360x+480-210x &= 300x-600+180&& \text{simplify left and right hand side} \\[1 em]150x+480 &= 300x-420&& \text{move the $ \color{blue}{ 300x } $ to the left side and $ \color{blue}{ 480 }$ to the right} \\[1 em]150x-300x &= -420-480&& \text{simplify left and right hand side} \\[1 em]-150x &= -900&& \text{ divide both sides by $ -150 $ } \\[1 em]x &= \frac{-900}{-150}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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