Is it possible to shoot yourself with either a hand gun or rifle or shotgun in your neck and head 4 times?

I suppose it's theoretically possible if you were to place a rapid-fire automatic weapon against your head and JAM your finger (or thumb) hard inside the trigger guard. Even so, the chances are that the recoil from the first shot would throw the weapon off target and 2, 3 and 4 would probably miss.

I don't think that's at all possible even with a small caliber rifle or pistol. No way with any shotgun. Too many vital areas that would be damaged with that many shots. A .22 will penetrate the brain easily and stay lodged in it. Let alone arteries or your larynx. Only a really lousy shot might possibly survive that but I very highly doubt it!

If you count "grazing" shots ... Yes, it's possible.
VERY difficult, and not probable ... But possible.