Fedora Core 6 ships with Firefox 1.5.x version. Firefox 2.0.x is currently in development repository of Fedora Core 6. So the command to update to Firefox 2.0.x browser is:

yum -y ––enablerepo=development update firefox

It also updates fedora-bookmarks and yelp. At around 21M it is a must upgrade. The current version as of today is 2.0.0.3-4.