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Location: Temple Reception Area, Fedris Hler
The first time you visit Fedris Hler in the Temple's Reception Area, you'll receive a quest from him. He believes King Helseth is training goblins for use in his army. Almalexia is worried that Helseth will lose control over the goblins and that they will attack the city. Your job is to kill the two goblin warchiefs, and while your at it, see if you can find and kill the two Altmer trainers as a bonus.
You can find the goblin army if you go down a trap door in one of the corners of Godsreach, enter the West Sewers, and from there find the entrance to the Battlefield. Once you're in, the two warchiefs are located in the area named "Tears of Amun-Shae." Find the two trainers by entering an area off the battlefield named "Teran Hall", and fall down through an invisible floor around the corner at the three way intersection to a room with goblins. Follow that corridor around to another door which leads you to the two tough trainers, Armion and Yarnar. They look like angry humans in armor and they'll double team you, so be prepared to use a few potions.
Your journal will be updated when you complete either of the two tasks, so report back to Fedris Hler when you're through looking around. If you manage to take the life from the Altmer trainers as well, he'll give you a very solid 15,000 gold, the largest gold reward in the game. Selling some of your named artifacts to the Museum Curator in Godsreach can get you even more, up to 32,000.
Speak to Hler once again and he'll tell you that Gavis Drin, Almalexia's head priest, wants a word with you. He's in the Lord Archcanon's section of the Temple, to the left of the entrance.