Mr. House asks the player to convince the Omertas to ally with Mr. House. The player can achieve this by completing How Little We Know, or killing all the Omertas. Upon doing either, the player must then return to Mr. House. If you have previously done either, the quest will mark as completed automatically. House will pay you anyway, just to avoid discouraging you. Alternatively, the player can just refuse to surrender his weapons upon entering the casino and thus turn the Omertas hostile. There is no need to kill any of them, leaving and speaking to House will fail the quest but allow the player to proceed to part 5. This is the fastest way to pass this section but forfeits the rewards.
If you have already finished How Little We Know by siding with Nero and Big Sal, then you will automatically fail part IV when talking to Mr. House, unless you can pass a [Speech Check of 50] and tell him the Omerta's plans and then say you infiltrated them in order to gain their confidence.
pcps3xbox360 After eliminating the Omertas, Mr. House doesn't recognize that they are gone. To remedy this, load a save point before killing Big Sal and Nero, go talk to Mr. House and make sure you go through all the dialogue on what to do about the Omertas. After this, killing Big Sal and Nero and returning to Mr. House should allow you to finish the quest.
xbox360 When working on Part IV of the mission, there will be an option while talking to the Omerta receptionist that says [Barter x/55], meaning you need at least 55 Barter to choose it. But upon using a Salesman Weekly to raise Barter to 55, the option goes away, and you are left with the [Strength x/8] option or the option to hand over 300 caps. Leveling up the Barter skill does not help.