$$ \begin{aligned} \frac{2}{3}(x+5)+6 &= 4x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{2}{3}(x+5)+3\cdot6 &= 3\cdot4x&& \text{cancel out the denominators} \\[1 em]2x+10+18 &= 12x&& \text{simplify left side} \\[1 em]2x+28 &= 12x&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 28 }$ to the right} \\[1 em]2x-12x &= -28&& \text{simplify left side} \\[1 em]-10x &= -28&& \text{ divide both sides by $ -10 $ } \\[1 em]x &= \frac{-28}{-10}&& \\[1 em]x &= \frac{14}{5}&& \\[1 em] \end{aligned} $$

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