The table below shows the distance d(t) in feet that an object travels in t seconds:

t
(second)

d(t)
(feet)

2

64

4

256

6

576

8

1024

what is the average rate of change of d(t) between 2 seconds and 6 seconds, and what does it represent?

The rate of change of d(t) at t = 2 and t = 6 is the ratio between the change of distance (difference between the distances) to the time elapsed. That is,
                                   r = (576 - 64) / (6 - 2) = 128 ft /s
The rate of change is equal to 128 ft/s and this represents the average speed at this time interval.