Let’s change this question to “which director had the hottest run of any length…who enjoyed the greatest cavalcade of grand-slam films, whether it was four or six or even ten?”
The answer in this instance would be Howard Hawks and his nine-year, nine-film run of one bull’s-eye after another…it began in 1938 with Bringing Up Baby and ended in 1946 with Red River (even if that classic western wasn’t released until ’48).
The rundown: Bringing Up Baby (’38), Only Angels Have Wings (’39), His Girl Friday (’40), Sergeant York (’41), Ball of Fire (’41), Air Force (’43), To Have and Have Not (’45), The Big Sleep (’45 and ’46) and Red River (shot in ’46, released in ’48).
If you want to be strict and keep it to four, I would say that Stanley Kubrick‘s Paths of Glory (’57), Spartacus (’60), Lolita (’62) and Dr. Strangelove (’64) was an extraordinary run.