Find the product of $0.\overline{6}$ and 6.
I notice that $0.\overline{6}$ is a repeating decimal, which means it can be written as a fraction using a clever trick. If I let $x = 0.\overline{6}$, then multiplying both sides by 10 gives $10x = 6.\overline{6}$. Subtracting $x$ from both sides, I get $9x = 6$, so $x = \frac{2}{3}$. Now I can multiply $\frac{2}{3}$ by 6 using the rule for multiplying fractions: multiply the numerators and multiply the denominators. This gives me $\frac{2}{3} \times 6 = \frac{2 \times 6}{3 \times 1} = \frac{12}{3} = 4$. So the product of $0.\overline{6}$ and 6 is 4. 