To help answer this question, let's solve it step-by-step.
1. **Initial Amount of Water**: Fariya starts with 80 gallons of water.
2. **Water Splashed Out by the Dog**: The dog splashes out 1/4 of the water, so we calculate the amount of water splashed out:
$$
\text{Water splashed out} = 80 \text{ gallons} \times \frac{1}{4} = 20 \text{ gallons}
$$
3. **Remaining Water After Splash**: To find out how much water is left after the dog's splashing, we subtract the amount splashed out from the initial amount:
$$
\text{Remaining water} = 80 \text{ gallons} - 20 \text{ gallons} = 60 \text{ gallons}
$$
4. **Water Gain Ratio**: Fariya then turns on the water, and the tub gains back 1/3 of the remaining water. Let's calculate the amount of water gained:
$$
\text{Water gained} = 60 \text{ gallons} \times \frac{1}{3} = 20 \text{ gallons}
$$
5. **Total Water After Gain**: We’ll add the water gained back to the remaining water:
$$
\text{Total water after gain} = 60 \text{ gallons} + 20 \text{ gallons} = 80 \text{ gallons}
$$
6. **Water Drained Out**: Now, she drains 4/7 of the water. We calculate the amount of water drained:
$$
\text{Water drained} = 80 \text{ gallons} \times \frac{4}{7} = \frac{320}{7} \text{ gallons} \approx 45.71 \text{ gallons}
$$
7. **Final Amount of Water**: Finally, we find out how much water is left after the draining by subtracting the water drained from the total water after the gain:
$$
\text{Remaining water} = 80 \text{ gallons} - \frac{320}{7} \text{ gallons} = \frac{560}{7} \text{ gallons} - \frac{320}{7} \text{ gallons} = \frac{240}{7} \text{ gallons} \approx 34.29 \text{ gallons}
$$
Since this is a multiple-choice question and the remaining water after the draining process must match one of the options, and none of the answer choices are in decimal or fraction form, let's look again at our calculation:
The last operation was to find out how much water remained after some of it was drained. We calculated that $\frac{240}{7}$ gallons remained. When we divide 240 by 7, we get 34 with a remainder, which indicates that the nearest whole number is 34. This does not seem to match any of the answers provided.
However, we are looking for the closest answer in the form of a whole number, as multiple-choice questions usually require. Among the options given a, b, c, and d, the number closest to our final amount is option d. 67, which does not make any sense with a calculated result of approximately 34.29 gallons.
Please double-check the options provided as they might contain a mistake, and let's focus on the correct final calculation, which is approximately 34.29 gallons.