1. **State the problem:** Simplify the expression $$\frac{8}{12} \times x^{-3} \div t^2 \times t^3 \div x^2$$. 2. **Rewrite the expression:** $$\frac{8}{12} \times x^{-3} \times \frac{t^3}{t^2} \times \frac{1}{x^2}$$ 3. **Simplify the coefficients:** $$\frac{8}{12} = \frac{2}{3}$$ 4. **Simplify the powers of $t$ using the rule $\frac{t^a}{t^b} = t^{a-b}$:** $$\frac{t^3}{t^2} = t^{3-2} = t^1 = t$$ 5. **Combine the powers of $x$ using the rule $x^a \times x^b = x^{a+b}$:** $$x^{-3} \times x^{-2} = x^{-3 + (-2)} = x^{-5}$$ 6. **Put it all together:** $$\frac{2}{3} \times t \times x^{-5} = \frac{2t}{3x^5}$$ **Final answer:** $$\boxed{\frac{2t}{3x^5}}$$