To find out how many miles Sonny walks after seven days, you can multiply the distance he walks each day by the number of days.
Sonny walks \( \frac{2}{3} \) of a mile each day.
After 7 days, the total distance he walks is:
\[ \frac{2}{3} \times 7 = \frac{2 \times 7}{3} = \frac{14}{3} \text{ miles} \]
Therefore, the correct answer is \( \frac{14}{3} \) miles.