To determine the constant of proportionality \( \frac{y}{x} \) (in this case, miles per hour), we need to use the information given about Julian's walking speed.
Julian takes 12 hours to walk 2 miles. To find his speed in miles per hour, we divide the distance by the time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ miles}}{12 \text{ hours}} = \frac{1}{6} \text{ miles per hour} \]
Thus, the constant of proportionality \( \frac{y}{x} \) in this situation is \( \frac{1}{6} \) miles per hour.