The door to Old Man Thon in the Missing Cows quest opens only after you progress the quest far enough to get the marker for him, then clear the enemies around his cabin. He’s southeast of the Enclave, and players report that the door can stay shut until the nearby hostiles are defeated.

What to do

  1. Finish the cow-return part of the quest.
  2. Speak to Lalage or follow the quest step that sends you to Old Man Thon.
  3. Go to the marked cabin southeast of the Enclave.
  4. Kill the enemies around the area, including any that may be slightly off to the side.
  5. Try the door again after the area is clear.

If it still will not open

  • Reload the area or the save, since some players report the door only unlocking after a clean reset.
  • Make sure you are at the correct cabin location, not just inside the general search circle.
  • If the quest text has not updated yet, you may need to advance the conversation chain first.

Quick note

This looks less like a special puzzle door and more like a quest-gated door tied to combat and progression.

TL;DR: clear the nearby enemies, make sure the quest has advanced to Old Man Thon, and then interact with the door again.