$$ \begin{aligned} \frac{4}{7}x+\frac{6}{7} &= -\frac{2}{7}&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{4}{7}x+7\cdot\frac{6}{7} &= -7\cdot\frac{2}{7}&& \text{cancel out the denominators} \\[1 em]4x+6 &= -2&& \text{ move 6 to the right } \\[1 em]4x &= -2-6&& \\[1 em]4x &= -8&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{8}{4}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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