$$ \begin{aligned} \frac{5}{6}+\frac{1}{2}(x+4) &= \frac{2}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot\frac{5}{6}+6\frac{1}{2}(x+4) &= 6\cdot\frac{2}{3}&& \text{cancel out the denominators} \\[1 em]5+3x+12 &= 4&& \text{simplify left side} \\[1 em]3x+17 &= 4&& \text{ move 17 to the right } \\[1 em]3x &= 4-17&& \\[1 em]3x &= -13&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{13}{3}&& \\[1 em] \end{aligned} $$

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