$$ \begin{aligned} 3x-6 &= \frac{2}{3}x+1&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot3x-3\cdot6 &= 3 \cdot \frac{2}{3}x+3\cdot1&& \text{cancel out the denominators} \\[1 em]9x-18 &= 2x+3&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -18 }$ to the right} \\[1 em]9x-2x &= 3+18&& \text{simplify left and right hand side} \\[1 em]7x &= 21&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{21}{7}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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