1. **State the problem:** Given the equation $4x - y = \frac{2}{3}$, find the value of $$\frac{81^{3x}}{27^y}$$. 2. **Rewrite the bases as powers of 3:** - $81 = 3^4$ - $27 = 3^3$ 3. **Express the expression using base 3:** $$\frac{81^{3x}}{27^y} = \frac{(3^4)^{3x}}{(3^3)^y} = \frac{3^{12x}}{3^{3y}}$$ 4. **Use the quotient rule for exponents:** $$\frac{3^{12x}}{3^{3y}} = 3^{12x - 3y}$$ 5. **Simplify the exponent:** $$12x - 3y = 3(4x - y)$$ 6. **Substitute the given equation $4x - y = \frac{2}{3}$:** $$3 \times \frac{2}{3} = 2$$ 7. **Final value:** $$3^2 = 9$$ **Answer:** 9 (Option B)