Does this patient have HHV6 or HCMV after transplant surgery?
I get the feeling that there's something we should probably know from your textbook or notes that you have not included. As-is, here's my best shot:


It is impossible to determine if Patient A was infected by the transplant since the virus they had before the transplant is the same virus carried by the transplant itself. Without running further tests to separate the two lineages you can't tell. It's likely, though.
While HHV6 has been known to precede HCMV in certain cases the conditions don't seem to apply here. My best guess, which is something I'm pretty loathe to say, is that if you're positive the tests are accurate then it's possible that Patient B's immune system alternately suppressed each virus below detectable levels. Since Patient B is receiving donor tissue with both viruses, and transplant patients are put on immunosuppressants following surgery, it could simply be that at first the immune system was capable of dealing with HCMV for the first week, but not HHV6. Then as it adapted to HHV6, HCMV evolved to evade so it showed up on the assays. That is entirely speculative, though. Another explanation might be that the viral titers of HCMV were too low to detect at Week 1, but it had reproduced enough to show up at Week 3 while the immune system dealt with HHV6. There's a lot of information that's missing on how the virii behave, the characteristics of the immunosuppressants given to the patient, and so on.
Patient C was clearly infected with nothing. They already had HHV6, and that's what showed up post-op. 
Patient D was infected with HHV6. They had HCMV before, and both after.
Patient E was infected with HCMV, although like Patient A they could have been infected with a different strain of HHV6 as well, but the tests probably aren't specific enough to determine viral lineages for the before and after strains.