Burn the White Hound is a contract in Mission 1 of Dishonored Death of the Outsider.
Mission 1 – One Last Fight has two contracts that can be completed without much deviation from the main mission. You receive them by looking at a piece of paper on your desk on the Dreadful Wale at the beginning of the first mission.
Burn the White Hound Walkthrough
From the bar area in Industrial Espionage, go through the opposite door onto the walkway that is above the boxing ring. Be sure to stay crouched on the off chance that someone sees you. Through the second door to your right will be an area with an Eyeless cleaning up some broken glass, moving back and forth. Take them out, and take note of the Boilers to your right. These will be right next to the stairway down that leads to the gate behind the counter next to the boxing ring. These boilers will be where you burn the White Hound’s body to complete the contract.
To get to the hound pens, from where you came into the room, turn left and go to the end of the room where you will find two doors. Ahead will be a room with some hook mines, to the left you will find a large room with two guards and the hound pens with three wolfhounds inside. One of them will be Milky, the white hound you have to deal with.
Take out the guards, then hit the button on the wall to the left of the cage to open the cage door, and take out all three hounds. Pick up Milky, and carry the white hound all the way back to the boilers in the previous room. Open the door, throw the body in, and press the red button between the boilers to activate them. Milky’s body will be incinerated, and your contract will be complete.