$$ \begin{aligned} \frac{5}{6}p-\frac{1}{4} &= \frac{2}{3}p+\frac{1}{12}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{5}{6}p-12\cdot\frac{1}{4} &= 12 \cdot \frac{2}{3}p+12\cdot\frac{1}{12}&& \text{cancel out the denominators} \\[1 em]10p-3 &= 8p+1&& \text{move the $ \color{blue}{ 8p } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]10p-8p &= 1+3&& \text{simplify left and right hand side} \\[1 em]2p &= 4&& \text{ divide both sides by $ 2 $ } \\[1 em]p &= \frac{4}{2}&& \\[1 em]p &= 2&& \\[1 em] \end{aligned} $$

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