"The dirty jacket is mine."
Translation:Den skitne jakken er min.
I believe it's because when using adjectives in the definite case, you change the adjective to its plural form ("rød bil" becomes "den røde bilen"), meaning "skitne" would have to be the plural form of "skitten" (keep in mind im not a native speaker and i might be wrong about this)
I think the hover-over audio is automated for many, if not all words. "den" sounds like "dn" at the end of words like hunden, so the algorithm seems to be using that rule for the word "den" as well. I reported it about 5 times, but I think whoever recorded the voice might be long gone.
The business about "already been introduced" only applies when using det/den as a pronoun. Don't confuse that with using it as a definite article, which is what we have here. In this sentence you must use "den" to agree with the noun "jakke". The definite form "the jacket" is "jakken". If we want to put an adjective before the noun, we need to precede that with another definite article (det/den). This gives us what is called "double definiteness". So, "the dirty jacket" becomes "den skitne jakken". So "den" here is functioning as the article "the" and needs to match "jakke". If I had a neuter noun, such as "hus", then "the house" is "huset" and "the dirty house" is "det skitne huset" ("det" because "hus" is neuter).
If I use det/den as a pronoun, then I can use "det" for unknown (unintroduced) things:
Person1: Hva er det? Det er skittent. (What is it? It is dirty.)
Person2: Det er jakken min. (It is my jacket.)
Now that the jacket has been "introduced", person1 might say:
Person1: Du må vaske den. (You have to wash it).
Note the differences when using det/den as a pronoun, and when using det/den as a definite article.