$$ \begin{aligned} \frac{1}{2}y+2\frac{3}{4}y &= \frac{1}{4}y+6&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{2}y+4\cdot2\frac{3}{4}y &= 4 \cdot \frac{1}{4}y+4\cdot6&& \text{cancel out the denominators} \\[1 em]2y+6y &= y+24&& \text{simplify left side} \\[1 em]8y &= y+24&& \text{move the $ \color{blue}{ y } $ to the left side} \\[1 em]8y-y &= 24&& \text{simplify left side} \\[1 em]7y &= 24&& \text{ divide both sides by $ 7 $ } \\[1 em]y &= \frac{24}{7}&& \\[1 em] \end{aligned} $$

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