This is the 644th most frequent Danish word.
eget
"Own" (possessive, neutral singular form).
Here, 'eget' means 'own' and is used as a possessive determiner to indicate ownership of the room by the subject.
Jeg har mit eget værelse.
I have my own room.
Here, 'eget' is used to emphasize that the house belongs to the subjects and not someone else, aligning with 'hus' (house) in singular and neuter form.
De byggede deres eget hus.
They built their own house.
In this sentence, 'eget' again denotes ownership or personal responsibility and agrees in gender and number with 'arbejde' (work).