1. **State the problem:** Simplify the expression $$(0.66x) \times \left(\frac{10}{0.77x}\right)$$. 2. **Write the expression clearly:** $$0.66x \times \frac{10}{0.77x}$$ 3. **Multiply the numerators and denominators:** $$\frac{0.66x \times 10}{0.77x}$$ 4. **Simplify the fraction:** $$\frac{0.66 \times 10 \times \cancel{x}}{0.77 \times \cancel{x}}$$ 5. **Cancel the common factor $x$ in numerator and denominator:** $$\frac{0.66 \times 10}{0.77}$$ 6. **Calculate the numerator:** $$0.66 \times 10 = 6.6$$ 7. **Divide numerator by denominator:** $$\frac{6.6}{0.77}$$ 8. **Perform the division:** $$6.6 \div 0.77 = 8.5714$$ (rounded to 4 decimal places) **Final answer:** $$8.5714$$