$$\frac{2c+6}{3} = 1+\frac{c}{6}$$

$$ \begin{aligned} \frac{2c+6}{3} &= 1+\frac{c}{6}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{2c+6}{3} &= 6\cdot1+6 \cdot \frac{c}{6}&& \text{cancel out the denominators} \\[1 em]4c+12 &= 6+c&& \text{move the $ \color{blue}{ c } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]4c-c &= 6-12&& \text{simplify left and right hand side} \\[1 em]3c &= -6&& \text{ divide both sides by $ 3 $ } \\[1 em]c &= -\frac{6}{3}&& \\[1 em]c &= -2&& \\[1 em] \end{aligned} $$

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