The sentence means that the rug appeared because they were in demand.
Accroding to this, the first version is incorrect as ''as a part of their need'' states that it is a part of rugs' need, which makes no sense. There should be a reason that explains why they were made. Next two sentences are wrong because the first one brings the same meaning as in the previous one but with another preposition, and what about the second one - it has opposite meaning to what we are looking for. Only the last one is totally correct because there is a represented reason of making rugs and sensible word order that doesn't make doubts.
D) The first rugs were made because of their need. ---- they were needed
