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Pheeble Will - Walter Phebus
You can find Walter Phebus and his wife Ethel walking around the outside of the NCR station and the Ultra-Luxe Casino. If you talk to Walter, you can ask about him and learn about his reason for coming to New Vegas. Even if you fail the persuasion test, he'll tell you that he's there tracking Heck Gunderson as he negotiates at the Ultra-Luxe. He wants to make him suffer, and we're in a good position to help.
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Pheeble Will - The Peaceful Way
If you don't want to kill Heck or Ted Gunderson, you can just use this path to wrap the quest up peacefully.
You can open this path by talking to Ethel and agreeing to help her convince Walter to abandon his quest for revenge. In order to get him to actually abandon it, you either need high perception or 75 points in Speech. If you can pass the Speech check, you'll be able to convince him that he should really just go home before he crosses the line.
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Pheeble Will - A Quick Hit
With this information, you can go back and talk to Walter. He'll want you to wipe out both of them. If you have 80 points in Barter you can convince him to pay a bit more or convince him to just be happy with killing one of the two Gunderson's (although it's just as easy to get both of them). If you're planning to do Beyond the Beef, I think it's best to just agree to it in general so that you get the money for both kills. It's up to you though and your own plans for assassination.
If you follow Beyond the Beef, just choose to use Ted for the meat of the meal. If you kill Ted and frame Heck for the murder, he'll die resisting arrest and you'll get credit for the kills. Note that if you rescue Ted and take him all the way to his father, you will automatically fail "Pheeble Will." Walter and Ethel will disappear from the game world and there just isn't anything else that you can do.
Note that if you want, there's nothing stopping you from using a stealth boy and some C4 to stealthily kill Heck in a more traditional way. A reverse pick pocketed mine will work too and even a stealthy sniping, though quite difficult, is an option. As long as you carry out your end of the bargain and make Heck suffer, you'll get a very rich payday for a very simple quest.
New Vegas is the heart of the Mojave Wasteland and is naturally a hub for many different quests. I'll tell you how to find some talent for the The Tops, break up a group of cannibals (or help them), help a rancher get revenge or do a little sightseeing across the Wasteland.