In this context, to show that two operators do not commute means that C D f(x) does not equal D C f(x). We are given one part of this equation, that C D f(x) = 4x, and since C = d/dx and D = x^2, we can say: d/dx ( x^2 f(x) ) = 4x. If we then integrate both sides can you get a general expression for f(x)? Don't forget the arbitrary constant! Then we can use f(x) to compute D C f(x) which will mean computing: x^2 ( d/dx f(x) ). If we can show that the result of that expression can't possibly equal 4x, no matter what we choose for the arbitrary constant, we can confidently say C and D do not commute.
