That is a prolapse she needs medical treatment. can you get her to a vet? You need to keep it moist you can also try and moisten it up and push it back inside use KY jelly or Vaseline or Prep H but check for an egg also. as fat as that looks might have an egg in still.
Separate her immediately from the flock to prevent pecking or nibbling.
I have no experience with prolapse in ducks or geese. But, I believe the procedure is same as chickens.
The procedure for chickens would be:
Carefully cleaning the prolapse with warm water or sterile saline solution, and then gently pushing it back into place
Apply Preparation H or witch hazel (which is a natural anti-inflammatory that will help tightens skin and vent, soothes and reduces pain and swelling)
or (Amelia Barrows of "Treating the Sick or Injured Chicken" recommends applying honey to the tissue, then, gently pushing it in. Honey will help hold everything together, fight infection and shrink tissues. She also recommends additional antibiotics till healed. May also, have to help remove additional eggs the hen may lay.
Keep her in a dark, quiet location to reduce the chances she will lay another egg (a dog crate with a blanket or towel draped over it works well).
Withhold feed for at least 24 hours but providing lots of fresh water.
Provide good supportive care: mainly greens and small meals of cooked grains, cooked egg, diced fruit
You may have to repeat the treatment until the prolapse has healed. You will have to be vigilant that the vent heals. There is always a chance that she will not recover, some hens require sutures to re-tighten the vent tissue, but do your best for her.
Please consider additional advice from other BYC members.