Looking at the complete text in the picture, there is no event in the past that "been together" can be placed before, so past perfect is incorrect in this context: it should be present perfect "have been", indicating that the two years extends until the present.
If some other event had occurred in the past and the two years was before that event, or the meeting had already occurred and this was an account of the meeting, the use of past perfect would be justified:
My brother announced his engagement on New Year's Eve: he and his fiancee had been together for two years. - the two years was before the announcement.
My brother and his fiancee had been together for two years. I couldn't wait to meet her. - account of a meeting that took place in the past
The later sentence "My parents already spent..." may be OK in American English, but British English would use present perfect for this too:
My parents have already spent time with her.
Present perfect is used when a past action is still in force or has some lasting effect, and in this case the lasting effect is that your parents have checked off spending time with her on their list of things to do.