The part about "I lost the tweezers, so we can't operate. But we can prep the guy!" is some kind of a joke, and does not actually sound like anything girls would say, seriously, in real life.

A "prep" may or may not involve shaving the hair on the lower body. It is embarrassing if you aren't expecting it. When people talk about a "prep" for an operation, this is sometimes what they mean.

Here it is just a joke--there is nothing you could do with an "Operation" game set that would resemble a "prep." The idea of the joke is "if we can't actually perform surgery on the guy, we can at least shave him."

Hi Eva,

You will get more responses if you post questions like these in the "Answers" section of Italki.  But I'll answer your question here :)

A duplex is a kind of apartment.  So Leslie is just exaggerating and saying something like "I'm as big as a house" or in this case, an apartment.

"Prep" stands for prepare.  When someone is going to have an operation, the nurses prepare him/her in advance.  So these ladies are going to play a (famous) board game called "Operation" where you have to take out the tiny body parts of a guy with little tweezers.* But since she lost the tweezers, they can only "prep" him. 

* [ http://www.amazon.com/Hasbro-4545-Operation-Game/dp/B00000DMFM/ref=sr_1_1?ie=UTF8&qid=1423397146&sr=8-1&keywords=operation]

And in the U.S., an apron can be the waist down type, or the whole body type.  We have only one word for both.

However, aren't they playing a board game called Operation. And I guess the patient is Sam the man drawed on the paper sheet. So I actually don't think that makes any sense

I meant I just have no idea about what they actually do when prepping a patient

Sorry for the inconvenience, but I'm just out of the two opportunities to post in the question section.