Assuming that Mathematica was installed in the default location, open a
shell and cd to /usr/local/Wolfram/Mathematica. There you will find the
installation for each version of Mathematica. Remove version 6 with "sudo
rm -rf 6.0" (no quotes). If you don't have su privelages then ask someone
who does. In addition a number of links are created in /usr/local/bin that
you may want to remove. Lastly in your home directory you will find a
.Mathematica directory which should contain your user installed packages
etc and customizations. Remove this if you want.
Cheers
Yas