What is the volume of a rectangular pool with a length of 46 feet and a width of 24 feet and a depth of 4 feet in the shallow end and 8 feet in the deep end?

I can answer that only IF the slope of the bottom is uniform ... it slopes continuously

from 4-ft at one end to 8-ft at the other end, with no level spots.

If that's true, then the average depth is 6-ft, and the volume is

46 x 24 x 6 = 6,624 cubic feet = 2451/3 cubic yards = 49,550.96 gallons.