You may need to rename the FC6 VolGroup since it probably clashes with the new fedora installation.
The steps are something like this:
Boot up into rescue mode using the FC6 install disk, it will probably list two Fedora targets, select the FC6 one (if you're not sure just guess, if it's wrong reboot)
Type lvscan & vgscan to list logical volumes and volume groups
You'll probably have VolGroup00/LogVol00 (root filesystem) and VolGroup00/LogVol01 (swap)
lvchange -a n VolGroup00/LogVol00
lvchange -a n VolGroup00/LogVol01
vgrename VolGroup00 VolGroup99