1. The problem is to subtract the fractions $\frac{2}{3}$ and $\frac{1}{2}$. 2. To subtract fractions, we need a common denominator. The denominators are 3 and 2. The least common denominator (LCD) is 6. 3. Convert each fraction to have denominator 6: $$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$$ $$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$ 4. Now subtract the numerators: $$\frac{4}{6} - \frac{3}{6} = \frac{4 - 3}{6} = \frac{1}{6}$$ 5. The fraction $\frac{1}{6}$ is already in simplest form. 6. Therefore, the answer is $\frac{1}{6}$.