$$ \begin{aligned} 2(x+\frac{2}{3}) &= 0&& \text{simplify left side} \\[1 em]2 \cdot \frac{3x+2}{3} &= 0&& \\[1 em]\frac{6x+4}{3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{6x+4}{3} &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]6x+4 &= 0&& \text{ move the constants to the right } \\[1 em]6x &= -4&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{4}{6}&& \\[1 em]x &= -\frac{2}{3}&& \\[1 em] \end{aligned} $$

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