I skipped over the bolded stuff. If you have learned about "deltas", then surely you have learned how to take the derivative of a function? The rate of change of a quantity with respect to another quantity, is simply the derivative. Here you are meant to calculate the rate at which the volume of an object is changing with respect to its dimension; so, using the simplified expression, find the derivative. Once you have the derivative, it is simply a matter of plugging in the values of the sides they give you, so that you may calculate the rate at which the volume is changing at a given side length.
If you are meant to take the difference quotient of this, the answer I get is . When taking the difference quotient, and then applying the limit as it approaches zero, your h's will cancel out, leaving you with an equation in x.