1. Stating the problem: Simplify the expression $$12 \cdot \left(\frac{2}{3}\right)^{-5} \cdot \left(\frac{2}{3}\right)^4$$. 2. Use the property of exponents: $$a^m \cdot a^n = a^{m+n}$$. 3. Combine the powers of $$\frac{2}{3}$$: $$\left(\frac{2}{3}\right)^{-5} \cdot \left(\frac{2}{3}\right)^4 = \left(\frac{2}{3}\right)^{-5+4} = \left(\frac{2}{3}\right)^{-1}$$. 4. Rewrite the negative exponent: $$\left(\frac{2}{3}\right)^{-1} = \frac{1}{\left(\frac{2}{3}\right)^1} = \frac{1}{\frac{2}{3}}$$. 5. Simplify the fraction: $$\frac{1}{\frac{2}{3}} = \frac{1}{\cancel{\frac{2}{3}}} = \frac{3}{2}$$. 6. Multiply by 12: $$12 \cdot \frac{3}{2} = \frac{12 \cdot 3}{2} = \frac{36}{2}$$. 7. Simplify the fraction: $$\frac{\cancel{36}}{\cancel{2}} = 18$$. Final answer: $$18$$.