Final answer:
The largest size of equal square tiles that can be used to make a checkerboard pattern on a floor measuring 128 inches by 96 inches is 32 inches per side.
Step-by-step explanation:
To create a checkerboard pattern on the given floor, we need to find the largest size of equal square tiles that can fit. The dimensions of the floor are 128 inches by 96 inches. We can find the largest size by finding the greatest common divisor (GCD) of these two dimensions, which is 32 inches. Therefore, the largest size of equal square tiles that can be used to make a checkerboard pattern is a square tile with a side length of 32 inches.