$$ \begin{aligned} x+4 &= \frac{2}{3}x+2&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3x+3\cdot4 &= 3 \cdot \frac{2}{3}x+3\cdot2&& \text{cancel out the denominators} \\[1 em]3x+12 &= 2x+6&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]3x-2x &= 6-12&& \text{simplify left and right hand side} \\[1 em]x &= -6&& \\[1 em]x &= -6&& \\[1 em] \end{aligned} $$

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