$$ \begin{aligned} \frac{1}{5}(3x+2)-\frac{1}{3}(x+4) &= 6&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{1}{5}(3x+2)-15\frac{1}{3}(x+4) &= 15\cdot6&& \text{cancel out the denominators} \\[1 em]9x+6-(5x+20) &= 90&& \text{simplify left side} \\[1 em]9x+6-5x-20 &= 90&& \\[1 em]4x-14 &= 90&& \text{ move -14 to the right } \\[1 em]4x &= 90+14&& \\[1 em]4x &= 104&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{104}{4}&& \\[1 em]x &= 26&& \\[1 em] \end{aligned} $$

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