Amazon Kindle Fire only supports azw/prc/mobi/tpz. Epub and pdf can not be natively accepted by Kindle Fire. So you need third-party program convert it.
You can google for example PDF MOBI CONVERSION to find programs (most are not free) to do that conversion. But note that some pdf's and epub's are protected by digital right management (drm). Our forum policies don't allow to discuss removing that.
If I have bought a new Kindle Fire, I may want to read all my favorite books on it. When you download the books,but I come across the books in the epub or pdf format. these two format are popular format of ebooks. The Kindle Fire does not support the two formats. So if I want to do so,what is the right process that can help me?