Rakothurz and Horm  

"All you have discovered will contribute to us keeping the Misty Mountains safer in the future. If our number was larger now, I have no doubt that Gloin would once again brave the depths of Goblin-town himself and destroy the goblins there. Alas, we are small in number, and there are greater threats to contain elsewhere. Let us be direct then....

'Gloin would like you to be watchful for the goblin and troll, Rakothurz and Horm, within the Great Goblin's throne room. Lord Elrond mentioned that the forces of Angmar wanted to draw them into the conflict in the north and west, and if we can destroy them we may save lives of countless allies.

'Search the throne room in Goblin-town for this troll and goblin, and after they are defeated, return to me. Goblin-town is far to the north and east.'

Information received from the letters you recovered in Black Speech led Gloin to offer rewards for the defeat of Rakothurz and Horm, a goblin-handler and a terrible Cave-troll found in the Great Goblins throne room in Goblin-town.

Objective 1
Defeat Rakothurz, Horm's Handler
Defeat Horm, the Pit Beast
Goblin-town is far to the north0east of Gloin's Camp and the throne room should lay straight through many tunnels

Tralli Gemfinder directed you to find and defeat the troll and goblin, Horm and Rakothurz, within the Great Goblin's throne room.