Manhunt/Border Patrol

Garage
When the cutscene finishes, you are alone in a room. You first need a weapon, obtained by breaking glass and taking the shard. Press the switch next to the garage door, and hide behind the Cerberus truck. One guard will follow you into the garage, and he will eventually turn around for you to perform the execution. There's other guards patrolling the garage area, but should be easier to eliminate with the pistol you picked up.

Proceed down the path. There is a gate which may be opened by a crowbar, or shot open with the pistol.

The garden ahead has a few enemies. At the other end is a save point.

Hedge garden
The cutscene shows snipers taking position on a balcony, but they only cover the main entrance rather than a side.

Enter the hedge maze, and turn left. Follow the left wall, and you will reach an open area with a few guards on patrol. The destination is at the far end of this area, where stairs lead down to a hedge maze ring. Guards tend to cluster around the stairs, which doesn't provide a good meant to pop in and out of cover during a firefight.

The center of the hedge maze contains a save point, which you may want to use before approaching the mansion.

Mansion
The ground level has several guards on patrol, some standing still, and some moving. You can hit one with a ranged weapon, and quickly fall back behind the corner from the hedge ring maze, which provides the cover of darkness.

The mansion has a small side entrance that leads to the balconies, allowing you to sneak up on the snipers from behind. Attacking them may cause the guards on the ground level to approach, but they can be defeated simply be taking cover behind one of the walls.

The proper entrance to the mansion is at the end of the path, which leads to a side door.