I would say that den generelle direktør corresponds to E. "the general manager". Typically, you'd see it in a football context: Jorge Valdano er klubbens generelle direktør (JV is the club's general manager). "Director-general", on the other hand, is generaldirektør in Danish: DRs nye generaldirektør, Maria Rørbye Rønn (DR's new director-general, MRR).
It has been noted by several actual Danes that no Dane would ever use this phrase: "Den generelle direktør," as there is no such title at all in the Danish language, even though when literally translated it means the General Manager or Director; and we do have general managers in English --- especially for professional sports teams. But the same position på dansk must be a title other than "den generelle directør". I believe this phrase is here to teach us that when the adjective is specific, as in this case, it takes the plural form. Therefore, please correct this phrase so that it teaches us the correct Dansk terms and title in the Danish language and not just a literal translation of the English.
Well, the title IS used: e.g.
-- Real-præsident Florentino Perez vil ansætte Hierro som erstatning for Jorge Valdano som klubbens generelle direktør"
-- "Arbejdsloven fastsætter yderligere begrundelsen for at afskedige den generelle direktør"
but not commonly, it's true (most references seem to be to the general managers of foreign football teams, or of other set-ups outside Denmark).
The leading director of a private compagny (CEO) is called 'den administrerende direktør'. 'Den generelle direktør' is not a title you will hear in Denmark, it does not exist! In some old, state-owned compagnies like the national railways, you still have the old title 'generaldirektør' (general ~ general as in the army!). Like in English you must distinguish between 1) generel = standard/common/regular and 2) general = high ranking officer. (I'm Danish!)
I wonder... Why is "generel" (the -el part") pronounced with an [a] sound, whilst "universel" is pronounced with an [ɛ] sound? The latter is true for "speciel", too.
Why is "generel" not spelled "general" then?
By the way, there is also "generaldirektør"... Perhaps, the exercise got it wrong...