Last Man Standing
You're not sure what Emil Marcone originally wanted you to do because you walked in on an ambush by the Verandi family. You managed to fight through the Family thugs and get to Emil, who swore that the Verandi family will pay for their attack.
Emil Marcone decided to retaliate by getting you to kidnap Vanessa Verandi, the daughter of Guido Verandi, head of the Verandi family in Port Oakes.
Emil Marcone had passed word that he had a reward for you at a warehouse, but it ended up being an ambush by Family there. You managed to fight through them and find a note from Emil Marcone to his lieutenant giving the order to take you out.
The Verandi and Marcone families had both decided to take you out. You decided to force a truce by capturing the heads of the Family to show that you can't be messed with. You found out where Guido Verandi makes his rounds and captured him, then did the same with Emil Marcone.
In the end, Guido Verandi and Emil Marcone agreed to call a truce, but their lieutenants had seized power. By taking down both Bloody Vicious and Pitbull you showed you were tougher than any Family in Port Oakes.