Equations 22-8 and 22-9 are approximations of the magnitude of the electric field of an electric dipole, at points along the dipole axis. Consider a point P on that axis at distance z = 6.00d from the dipole center(where d is the separation distance between the particles of the dipole). Let E_appr be the magnitude of the field at point P as approximated by Equations 22-8 and 22-9. Let E_act be the actual magnitude. By how much is the ratio E_appr/E_act less than 1?

The equations for this question are described in great detail on page 636 in Halliday, Resnick and Walker; you should read this page carefully.  Specifically, equations 22-5, 22-6, and 22-7 are all different ways to express the formula for the exact, NOT approximated electric field on the axis of a dipole, what this question calls E_act.  But the whole reason for treating a dipole as a special object is that at points "far" from the dipole, the electric field is given approximately by the simpler equations 22-8 and 22-9, which this question calls E_appr.

Philosophical Note: It may surprise you to hear, but the goal of Physics is NOT to calculate everything to the highest possible precission.  Rather, the goal is to be able to calculate results as acurately as needed, depending on what you need the result for.

If the approximation is any good, then the results of those equations should be nearly equal, so that the ratio E_appr/E_act is nearly one.  The question hints at the fact that actually the approximation is a bit smaller than the acutal field, so that the ratio is less than one.  Thus, the question is asking you to enter (1−E_appr/E_act).

The only mathematical trick to this is that both q and d are unknown.  But if you do the algebra, you should find that they cancel out of the final result.  If you need help with how this cancelation happens, please come to office hours or make an appointment.