"en jakke" is an indefinite, singular, common gender noun. Therefore the colour brown, an adjective, has no ending: "brun"
Danish: An Essential Grammar, 2nd Ed - main rule for indefinite declension:
[paragraph 18.104.22.168.] Adjectives agreeing with common gender nouns in the singular have no ending (‘zero’ ending, marked for convenience as ⊗), those agreeing with neuter singular nouns add -t, and those agreeing with plural nouns add -e
According to the rule above, in the indefinite declension, adjectives that agree with plural nouns (of both genders) add an -e: "brune".
There are some exceptions to the main rule for indefinite declension, and separate rules for definite declension.
Other Duo exercises for indefinite declension:
- brune bjørne = brown bears [plural so "brune"]
- Drengen spiser brune ris i august og september. = The boy eats rice in August and September. [ rice as collective/plural noun so "brune"]
- Den brune bjørn spiser et brunt jordbær. = The brown bear eats a brown strawberry. [ singular, neuter indefinite strawberry so "brunt"]
Note there is a separate rule for "Den brune bjørn" - the adjective is declined the same as the plural form for both common and neuter gender nouns when there's a definite article.