"Locuința lui are acoperișul roșu și garaj."
Translation:His dwelling has a red roof and a garage.
You can also say:
Locuința lui are (un) acoperiș roșu și (un) garaj.
Basically, we can use the definite article to indicate possession:
Close your eyes! - Închide ochii!
She's got a broken nose. - Ea are nasul spart.
He's got a phone with a broken screen. - El are un telefon cu ecranul spart.
If it's any clearer, you can translate it as "he's got a phone with its screen broken".
In English, saying "his dwelling has the red roof" suggests that there are some known roofs and the speaker makes a connection between "his dwelling" and one of them. Translated into Romanian, there'd be no difference in form between the two sentences; the distinction is based on context, but the most intuitive interpretation is the one in which the definite article represents possession.