$$V = lwh$$
where $$l$$ is the length, $$w$$ is the width, and $$h$$ is the height. In this case, we have $$l = 48$$ inches, $$w = 16$$ inches, and $$h = 12$$ inches. So, the volume of the rectangular prism is:
$$V = (48)(16)(12) = 9216 \ inches^3$$
Now, we need to convert cubic inches to gallons. There are 231 cubic inches in a gallon. So, the number of gallons of water to fill the rectangular prism is:
$$\frac{9216 \ inches^3}{231 \ inches^3/gallon} \approx 40 \ gallons$$
Therefore, we will need approximately 40 gallons of water to fill the rectangular prism.