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This is the second part of the Blackwater Park Mission in Hitman: Absolution which is called The Penthouse. In it you eliminate Layla and locate the panic room. This guide explains how to complete this mission on the hardest, purist, difficulty. It does not explain how to complete the different challenges in this area.
At the start just follow the ledge and drop down. Follow the corridor until you get to a door. Crouch walk through the door and take cover on the display case just past the door. Wait for the guard ahead to have gone out of sight to the left, then follow her. At the end of that corridor take cover on the left wall and wait for the large group of guards ahead to have gone off to the right into another corridor.
Follow the group until you get to the end of that corridor. Take cover on the chest of drawers. Eventually two of the three guards in sight will go off to the left, but one will turn towards you and stand guard at the entrance to the room.
Once he turns around subdue him and take his outfit. Then drag him into the next room and hide him in the wooden crate. Go back into the room you subdued the guard in. In that room is a desk with a monitor on it. Next to the monitor is a key card, be sure to take it. Go back down the corridor from earlier. In the room the group of guards you had to wait for earlier were in are stairs. Go up the stairs and through the door to the left at the top of the stairs. You don't need to worry about avoiding the lasers since the outfit allows you to be in that room. Go to the other side of the room and pick up the U'wa tribe poison.
Then go back out of the room. As you do two guards enter the room, don't worry about them they won't detect you. Go back into the first large room you entered. On the table in the middle of that room is a plate with sushi on it. Poison the sushi and turn left and go out of the door ahead to the balcony. Take cover on the other side of the table ahead and wait for Layla to come out onto the balcony and lean on the railing. As soon as she does push her off the ledge.
This will cause a silent and signature kill on Layla. Follow the balcony all the way around the building until you get to a door near the other end of the balcony. Go through it and towards the door with the key card scanner next to it. Use the key card you picked up earlier and go through that door. Follow the corridor and turn left at the end of it. Approach the part of the wall that is on an angle. It is a door. Go through it and pick up the phone that is on the bed. Once you have done that it is the end of this part of the mission, and indeed the whole mission.