One of the side quests that you will get during your stay at Monarch is A family Matter. It is revolves around a missing person. This page of the guide to The Outer Worlds has a walkthrough for this quest.
List of objectives
- Find Tucker Needham at Amber Heights;
- Convince Tucker to come home
As you travel through Stellar Bay, you will come across Agnes Needham. If you talk to her you will learn that her son is missing and was last seen headed towards Amber Heights. You will also be asked for help.
If you decide to help the woman, you need to go the location she mentioned. To get there, you only need to follow the road and avoid groups of marauders (or fight them). It's an Iconoclast camp. When you go inside, Rose will welcome you. Ask her about Tucker - and you'll know that the man can be found at the resort.
Find him and talk to him-you will learn that he was tired of his mother and decided to leave. At this point, you can try to convince him to come back or accept his decision and tell his mother that he died.
No matter how the conversation goes, you have to go back to Agnes and talk to her. Thus, you will finish the task.