It's the (virtual) framebuffer, which is enabled or disabled in your kernel. You can probably change the resolution of the framebuffer by adding a special parameter to your bootloader's kerner line, which tells the kernel to use specific resolution. This depends on your bootloader, but you're probably using GRUB if you're using Fedora Core 6.
If I'm right, the option you pass to the kernel is vga=value where value depends on the resolution you wish to use.
There are surely tables on the web that show all the possible values (which are three-digit values) for different resolutions and colour depths. I think for 800x600 resolution you could use value 788 or 789, so the option would be vga=788 for example.
You can first try this before saving any changes. Reboot your pc, when GRUB pops up you either get it's boot menu or press ESC (when asked to) to see the menu. Select the kernel you wish to boot (default should be selected, so no need to change..) and hit 'e' button to edit the boot lines. Hilight the line that starts with 'kernel' and press 'e' again to edit it. If the line already has a 'vga=something', edit that, or if it doesn't, simply add the 'vga=788' somewhere on the line, separated by spaces. Press enter and hit 'b' button to boot that kernel, and see if it is what you want..
When you want to save that setting, edit your GRUB configuration; become root ('su' in terminal, for example), launch a text editor and edit the file /boot/grub/menu.lst -- in that file locate the line(s) that start with kernel, and either add the vga=788 somewhere in the line, or edit an existing value if needed. Save and exit - that's it.