Can anyone help me with this?

Let f be a continuous function on [0,4]. Show that there must be values c and d in [0,4] such that:

c - d = 2 and f(c) - f(d)= [f(4) - f(0)]/2

I have been struggling with this one for a while now. The best thing I can think of is to split [0,4] into two intervals and use the IVT to show that f(c) and f(d) exist, but I don't know how the fact that their difference is the average of the interval affects things. Thanks.