Find the rate of change between the two points (4, 36) and (8,108) and give the unit of measure.

x is measured in square yards.
y is measured in dollars.

I know how to find the rate of change but I have no idea what they mean by "unit of measure." How do you find that?

the units would be dollars/yd^2

The rate of change is always ∆y/∆x, so the associated units just follow along.

y might be the cost (dollars) of some quantity x (yd^2) of carpet.