$$2p+\frac{6}{5} = \frac{5}{4}p-\frac{9}{5}$$

$$ \begin{aligned} 2p+\frac{6}{5} &= \frac{5}{4}p-\frac{9}{5}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20\cdot2p+20\cdot\frac{6}{5} &= 20 \cdot \frac{5}{4}p-20\cdot\frac{9}{5}&& \text{cancel out the denominators} \\[1 em]40p+24 &= 25p-36&& \text{move the $ \color{blue}{ 25p } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]40p-25p &= -36-24&& \text{simplify left and right hand side} \\[1 em]15p &= -60&& \text{ divide both sides by $ 15 $ } \\[1 em]p &= -\frac{60}{15}&& \\[1 em]p &= -4&& \\[1 em] \end{aligned} $$

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