Most DVD authoring software transcodes the input file (your 12gb) file to fit the dvd you burn it to (4GB).
The bigger the file the more compression it will need to fit on a standard dvd, most likely presenting itself as lower quality when viewed from the dvd.
ie. files around the size of the media you are burning it to will remain at a higher quality than files that are much larger than the media.
Can i ask one thing? What resolution is your Movie? Most likely an SD project as they can be very big when in an uncompressed format, but thought i would ask just in case.
If it is an HD resolution then it would only fit on a BluRay (or HD DVD, but they are pretty much dead!).
To achieve the highest quality i recommend dropping it into a program such as iDVD at its full file size (12GB) and leaving it to transcode and burn to the dvd you intend on using (4GB). I wouldnt suggest exporting it in a compressed format as you still need to further compress (transcode) the file to fit on the dvd, causing another generation of quality loss.
Try it with the file you have, i think you will be surprised. Trust me i managed to fit an 8.5GB file onto a 4GB dvd and the movie length was 5 minutes.