Are you trying to install FCP 6 on the Mac OS X10.7.5 system listed below your message?
That won't work unless you first install Rosetta from a Mac OS X 10.6 DVD.
If you pass that test and the disc really is physically damaged, you might try making a disk image of the DVD in Disk Utility. Use the DVD/CD Master format.
Obtaining a FCP 6 disc set will be difficult. Apple stopped making it years ago. Maybe used on eBay or Amazon.
do some googling on cleaning cd/dvd's.
Something like this?
I bought a cd/dvd cleaner at radio shack years ago that saved my butt a number of times. Unfortunately, I have no idea where it is.
And Nick's right (like he usually is) that making a disk image and then mounting it, is a good first step to see if the physical dvd is the problem.