$$ \begin{aligned} 6-\frac{2}{3}(x+5) &= 4x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot6-3 \cdot \frac{2}{3}(x+5) &= 3\cdot4x&& \text{cancel out the denominators} \\[1 em]18-(2x+10) &= 12x&& \text{simplify left side} \\[1 em]18-2x-10 &= 12x&& \\[1 em]-2x+8 &= 12x&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 8 }$ to the right} \\[1 em]-2x-12x &= -8&& \text{simplify left side} \\[1 em]-14x &= -8&& \text{ divide both sides by $ -14 $ } \\[1 em]x &= \frac{-8}{-14}&& \\[1 em]x &= \frac{4}{7}&& \\[1 em] \end{aligned} $$

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