If the original 18,000 gal of water is draining at a rate of 450 gal/day, we begin by calculating how many gal it needs to drain:
18,000-6,000 = 12,000 gal
Now setup 12,000 gal/1 × 1 day/450 gal, in order to cancel out gallons and have our result in days.
So 12,000/450 = 240/9 = 26.66 days, or a full 27 days rounding to the day