"The general director."
Translation:Den generelle direktør.
Because of the definite article. When you have the construction of "[Definite Article] [Adjective] [Noun]", the adjective always takes the "e-form"
Et stort hus = A big house
Det store hus = The big house
Huset er stort = The house is big
The same applies to common gender as well
En smuk pige = A beautiful girl
Den smukke pige = The beautiful girl
Pigen er smuk = The girl is beautiful
"Den generelle direktør" makes no sense in Danish. In Danish, the leader of an institution, an NGO, a non-profit etc. is called "generaldirektør", "direktør" or "formand".
And is there even such a thing as a "general director" in English? Shouldn't it be "director general"?
Actually, now I think about it, you're right. You can have a director-general (e.g. Director-General of the BBC) and a general manager (both different things) in English, "a general director" does make some sort of sense in the context of a usual director, but I can't really imagine what that would be anyway. Though I'm so clued up on business titles which is probably why this didn't seem too odd when I first read the English