$$ \begin{aligned} x-\frac{2}{3} &= \frac{4}{5}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15x-15\cdot\frac{2}{3} &= 15\cdot\frac{4}{5}&& \text{cancel out the denominators} \\[1 em]15x-10 &= 12&& \text{ move -10 to the right } \\[1 em]15x &= 12+10&& \\[1 em]15x &= 22&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{22}{15}&& \\[1 em] \end{aligned} $$

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