Over which interval does h have a positive average rate of change

In every case, the first given x is smaller than the second given x (e. g., in A, x=0 is smaller than x=6.  Thus, the change in x from 0 to 6 is positive.  

A:  Evaluate f(0) and f(6):  results are 0 and -9.  We see that the change in the function value from x=0 to x=6 is negative, so A is not an answer.

B:  Evaluate f(6) and f(8):  We get -9 and 0.  This is a positive change, so B could be an answer to this question.

C.  We already have f(0) and f(8); they are 0 and 0.  Thus, there is no net change in the function as we progress from x=0 to x=8.  C is not an answer.

D.  f(0) = 0, and f(2) = -3.  Here the function decreases, so D is not an answer.  

the function has a positive average rate of change from x=6 to x=8, and so the correct answer to this question is B.