Let the distance to the bike shop be $d$ miles. Then the time going is $\frac{1}{3}d$ hours and the time returning $\frac{1}{12}d$ hours. The total time travelling is therefore $\frac{1}{3}d+\frac{1}{12}d=\frac{5}{12}d$ and the total distance is $2d$ miles giving the average speed as $\frac{2d}{\frac{5d}{12}}=\frac{24}{5}$ miles per hour.