It’s become a common question right now that why FireFox 2 is not available on the Fedora Core 6 default package repositories? The answer seems to be on the FireFox 2 page of the Fedora Project Wiki. A small quote from this page:
For a variety of reasons, we are not planning to update to Firefox 2.0. We are instead focusing resources on Firefox 3.0, which will provide much more substantial benefits. We understand that some users will be willing to accept the risk of running Firefox 2.0 to gain compatibility with new extensions (e.g., Zotero and Halfnote). We have made available an experimental version of Firefox 2.0. However, we must stress that we believe the best experience for Fedora users will be to stay with Firefox 1.5 and wait for the Firefox 3.0 update. The experimental development version is available here:
http://people.redhat.com/caillon/RPMS/fc7/
You can also install the development version. Warning: This might result in instability.
$ yum --enablerepo=development install firefox
There are alternative ways posted over the Internet to install FireFox 2 onto Fedora Core 6, Jason Burns writes about one of them.