Translation:That is a price that I can afford.
It is "de prijs", therefore when referring back to it you need to use "die". The "dat" at the beginning of the sentence is simply to specify which price you are talking about, in this context. "Veroorloven" is a reflexive verb, so it requires the additional pronoun (i.e. "me", "zich", "ons" etc. depending on who it involves)