1. **State the problem:** Simplify the expression $$\frac{6x^3y^4}{12y^4x^2}$$. 2. **Write the formula and rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{6}{12} = \frac{\cancel{6}}{\cancel{12}} = \frac{1}{2}$$. 4. **Simplify the variables:** - For $x$: $$\frac{x^3}{x^2} = x^{3-2} = x^1 = x$$. - For $y$: $$\frac{y^4}{y^4} = y^{4-4} = y^0 = 1$$. 5. **Combine the simplified parts:** $$\frac{6x^3y^4}{12y^4x^2} = \frac{1}{2} \times x \times 1 = \frac{x}{2}$$. **Final answer:** $$\frac{x}{2}$$