$$ \begin{aligned} \frac{1}{7}(3x+2)-\frac{1}{5}(x+4) &= 2&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35 \cdot \frac{1}{7}(3x+2)-35\frac{1}{5}(x+4) &= 35\cdot2&& \text{cancel out the denominators} \\[1 em]15x+10-(7x+28) &= 70&& \text{simplify left side} \\[1 em]15x+10-7x-28 &= 70&& \\[1 em]8x-18 &= 70&& \text{ move -18 to the right } \\[1 em]8x &= 70+18&& \\[1 em]8x &= 88&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{88}{8}&& \\[1 em]x &= 11&& \\[1 em] \end{aligned} $$

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