$$\frac{1}{4}p+10 = \frac{1}{2}(p+4)$$

$$ \begin{aligned} \frac{1}{4}p+10 &= \frac{1}{2}(p+4)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}p+4\cdot10 &= 4 \cdot \frac{1}{2}(p+4)&& \text{cancel out the denominators} \\[1 em]p+40 &= 2p+8&& \text{move the $ \color{blue}{ 2p } $ to the left side and $ \color{blue}{ 40 }$ to the right} \\[1 em]p-2p &= 8-40&& \text{simplify left and right hand side} \\[1 em]-p &= -32&& \text{switch signs on both sides} \\[1 em]p &= 32&& \\[1 em] \end{aligned} $$

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