To find out how many bottles Jenny can fill, we need to divide the total amount of sports drink by the capacity of each bottle.
Jenny has 4 gallons of sports drink, and each bottle holds \( \frac{1}{8} \) of a gallon.
We can calculate the number of bottles by performing the following division:
\[ \text{Number of bottles} = \frac{\text{Total gallons}}{\text{Gallons per bottle}} = \frac{4 \text{ gallons}}{\frac{1}{8} \text{ gallon/bottle}} \]
Dividing by \( \frac{1}{8} \) is equivalent to multiplying by 8:
\[ \text{Number of bottles} = 4 \times 8 = 32 \]
Therefore, Jenny can fill \( \boxed{32} \) bottles.