1. **State the problem:** Simplify the expression $$\frac{16y x^4}{6x^8 y^2}$$. 2. **Write the formula and rules:** When simplifying fractions with variables, divide coefficients and subtract exponents of like bases using the rule $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify coefficients:** $$\frac{16}{6} = \frac{\cancel{16}^{8}}{\cancel{6}^{3}} = \frac{8}{3}$$. 4. **Simplify the variable $x$:** $$\frac{x^4}{x^8} = x^{4-8} = x^{-4} = \frac{1}{x^4}$$. 5. **Simplify the variable $y$:** $$\frac{y}{y^2} = y^{1-2} = y^{-1} = \frac{1}{y}$$. 6. **Combine all parts:** $$\frac{8}{3} \times \frac{1}{x^4} \times \frac{1}{y} = \frac{8}{3x^4 y}$$. **Final answer:** $$\frac{8}{3x^4 y}$$