$$ \begin{aligned} 4 \cdot \frac{2y+1}{5} &= 2y+\frac{6}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot4 \cdot \frac{2y+1}{5} &= 5\cdot2y+5\cdot\frac{6}{5}&& \text{cancel out the denominators} \\[1 em]8y+4 &= 10y+6&& \text{move the $ \color{blue}{ 10y } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]8y-10y &= 6-4&& \text{simplify left and right hand side} \\[1 em]-2y &= 2&& \text{ divide both sides by $ -2 $ } \\[1 em]y &= -\frac{2}{2}&& \\[1 em]y &= -1&& \\[1 em] \end{aligned} $$

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