There are no gallons of water at all in a pool which is 18 feet by 48 inches deep. In order to contain something, you need three dimensions, not just two.
However, let's assume that you meant a round pool with a diameter of 18 feet and a depth of 48 inches. That pool would contain 7614.23499 gallons.
The radius equals the diameter / 2.
The area of such a pool is pi * radius squared.
The volume of the pool is the area * depth.
Radius = 18 feet / 2 = 9 feet
Area = 3.14159 * 9 feet * 9 feet = 254.46879 feet squared (or square feet)
Volume = 254.46879 feet squared * 4 feet = 1017.87516 feet cubed (or cubic feet)
One liquid gallon is defined as 0.133 680 555 cubic feet (Authorized tables, U.S. Code, Title 15, ch. 6, subchapter I, sec. 205, accessed 19 July 2008.)
Therefore,
1017.87516 cubic feet * (1 gallon / 0.133 680 555 cubic feet) = 7614.23499 gallons
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17,204 gallons.
About 15,293 gallons.
About 7,600 gallons
15,954 US gallons of water.
Approx. 20k gallons.