I'm trying to install Fedora Core 6 on a USB drive.
Is that a typo? Looking at the link below at the Fedora site, you can see that support for that release ENDED 8+ years ago.
If you go to the Fedora site at the link below you will see the quote below:
Fedora 18 does not support UEFI booting for 32-bit x86 systems.
Since the iso you indicate you have downloaded is obviously 32bit that is going to be a problem.
Any particular reason why you don't use the currently supported Fedora?
Did you try mounting the actual Fedora iso? FC-6-i386-DVD.iso
Create the mount point in the directory in which you have the iso then loop mount it.