It seems as if he was discharged in 1978.
Why the additional six years?
Based only on what's seen here, it looks like he signed up for another six years. Probably in the Active Reserve, which he promptly ignored. He came from a prominent blueblood family. He may not have a desertion behind him (as they accuse W of having), but he may have had to get his service record "touched up" for those missing years, which is why they're off-limits to us.
It also means he was still a commissioned officer while he was hob-nobbing with the North Vietnamese.