They'll lead you to an Auto Eroticar showroom in Alderney; keep your distance from the place when they first pull in, as its swarming with enemies.
You could probably wipe most of the enemies out with an RPG or Grenade by blowing up the cars parked in the lot.
Then, head down the hall beyond the desk and enter the room where Anthony is being treated.
When the guest leaves, unplug the life support machine next to his bed and stand by while he kicks the bucket.
Drive Pegorino back to his place to complete the mission. The Pavanos are headed to a meeting, so start following them there.
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The Pavanos then attempt to make off with Pegorino's tribute, so you're going to have to follow them and get it back.
Pursue the Pavanos until they crash, then kill all four of them and pick up the tribute.
Fight your way to the car you used to drive in and take off.
There is a spray shop a short ways north from the hospital if you want to go for that, but it will only work if the police do not see you enter.