The correct answer is "moved".
Explanation:
The sentence requires the past simple tense because of the phrase "three days ago". Past simple tense is used to describe completed actions in the past. The verb "move" in the past simple is "moved". Therefore, the correct sentence is "They moved to a new flat three days ago."
Translation:
Они переехали в новую квартиру три дня назад.
So the correct option is:
* moved