$$ \begin{aligned} 2-\frac{3}{x}+4 &= \frac{12}{x^2}&& \text{multiply ALL terms by } \color{blue}{ xx^2 }. \\[1 em]xx^2\cdot2-xx^2\cdot\frac{3}{x}+xx^2\cdot4 &= xx^2\cdot\frac{12}{x^2}&& \text{cancel out the denominators} \\[1 em]2x^3-3+4x^3 &= \frac{12}{x^1}&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot2x^3-x^1\cdot3+x^1\cdot4x^3 &= x^1\cdot\frac{12}{x^1}&& \text{cancel out the denominators} \\[1 em]2x^4-3x+4x^4 &= 12&& \text{simplify left side} \\[1 em]6x^4-3x &= 12&& \text{move all terms to the left hand side } \\[1 em]6x^4-3x-12 &= 0&& \\[1 em] \end{aligned} $$

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