As with several other quests in the game, you can use social skills, stealth, or combat to get what you need here. It just so happens that the Giovanni are having a private reunion and nobody is getting into the mansion without an invitation.
This quest has you traveling to the Giovanni Stronghold to obtain the Ankaran Sarcophagus, if they have it. The Italian Dinner quest is triggered after you take Gary's phone call at the end of the I Spy Barabus quest.
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