Let $x = 0.\overline{6}$. Multiplying both sides by 10 gives $10x = 6.\overline{6}$.
Subtracting these equations, we get $9x = 6$, so $x = \frac{6}{9} = \frac{2}{3}$.
Therefore, $6 \div 0.\overline{6} = \frac{6}{\frac{2}{3}} = \frac{6 \cdot 3}{2} = \boxed{9}$.
The answer is: 9
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Determine the value of $6 \div 0.\overline{6}$.

### Answer:
