Sabotage Becky's still
What? A still! Damn. Hey, here's the $100, and I'll pay you $500 to destroy it. You can use my crowbar, in the back room over there. That'll do a number on her stupid little still!”— Frankie
Go to Becky's bar, on the other side of town. Go down the stairs and use a crowbar on the still. Go back to Frankie and receive the reward. Once you've destroyed the still, Becky won't talk to you anymore, so make sure you've done all of her quests before completing this one.
Alternatively, Frankie can be persuaded (Speech check) to buy his inventory from Becky, which awards 900 XP and +70 Karma.
You can convince Frankie to buy his liquor from Becky even after receiving your reward for destroying the still, this will get you both experience rewards for a total of 1600 XP. [verification overdue]
In v1.0 Becky will accuse you of destroying her still and stop talking to you even if you convince Frankie to buy whiskey from her. [verified]