From what region do Thorin's dwarf reinforcements come?

Thorin’s dwarf reinforcements come from the Iron Hills.

After Thorin and his companions reclaim the Lonely Mountain, he sends a message to his kinsman Dáin Ironfoot. Dáin rules the Iron Hills, a dwarf region to the east of Erebor, and responds by marching with an army of dwarf warriors.

The reinforcements arrive when conflict is building between Thorin’s dwarves, the Wood-elves and the people of Lake-town. Thorin refuses to surrender treasure to settle their claims, so the arrival of Dáin’s forces strengthens the dwarves’ position and makes a battle appear likely.

The dwarves from the Iron Hills do not fight the expected siege against the other claimants. Gandalf warns that goblins and Wargs are approaching, forcing the rival groups to unite against a larger common enemy. Dáin’s army then forms one of the forces involved in the Battle of Five Armies.

The Grey Mountains and Misty Mountains are nearby Tolkien locations, which makes them easy mix-ups. The Iron Hills, however, are specifically associated with Dáin and Thorin’s reinforcements.