$$\frac{4}{y+4} = -6$$

$$ \begin{aligned} \frac{4}{y+4} &= -6&& \text{multiply ALL terms by } \color{blue}{ y+4 }. \\[1 em](y+4)\cdot\frac{4}{y+4} &= (y+4)\cdot(-6)&& \text{cancel out the denominators} \\[1 em]4 &= -6y-24&& \text{ swap the left and right side of the equation } \\[1 em]-6y-24 &= 4&& \text{ move -24 to the right } \\[1 em]-6y &= 4+24&& \\[1 em]-6y &= 28&& \text{ divide both sides by $ -6 $ } \\[1 em]y &= -\frac{28}{6}&& \\[1 em]y &= -\frac{14}{3}&& \\[1 em] \end{aligned} $$

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