Step 1 :First, we need to convert the area from square inches to square feet because the coverage of the paint is given in square feet. There are 144 square inches in a square foot. So, we divide the total area in square inches by 144 to get the area in square feet. The calculation is \(\frac{76320}{144} = 530\) square feet.
Step 2 :Then, we divide the total area in square feet by the coverage of the paint to get the number of gallons needed. The calculation is \(\frac{530}{400} = 1.325\) gallons.
Step 3 :Since Becky can only buy whole gallons, we will round up to the nearest whole number if necessary. So, Becky needs 2 gallons of paint.
Step 4 :Final Answer: Becky should buy \(\boxed{2}\) gallons of paint.