1. **State the problem:** Jill starts with a full pail containing 2 gallons of water. On her way back, she loses half a quart of water. We need to find out how much water she manages to bring home. 2. **Convert units:** Since the pail's capacity is given in gallons and the lost water is in quarts, convert quarts to gallons for consistency. Recall that 1 gallon = 4 quarts. Therefore, half a quart = $\frac{1}{2}$ quart = $\frac{1}{2} \times \frac{1}{4}$ gallons = $\frac{1}{8}$ gallons. 3. **Calculate remaining water:** Subtract the lost water from the initial amount. $$\text{Water brought home} = 2 - \frac{1}{8} = \frac{16}{8} - \frac{1}{8} = \frac{15}{8} = 1.875$$ gallons. 4. **Final answer:** Jill managed to bring home $1.875$ gallons of water.