Only he's not asking if "You dig?"
Carter is bent on finding the truth by using the traditional action movie method of kill first and don't ask any questions at all. The movie rolls along like a semi sent straight from hell, bent on demonstrating that two wrongs don't make a right ... unless one of those wrongs is brutally murdering dozens of mobsters. In a film described by Roger Ebert as, "chock full o' corpses," narrowing down just one moment that encapsulates all that is Stallone is a heavy burden. But, like Jack Carter, we will let nothing stand in our way.
In a cruel joke, the Stalloneyest scene has been split in twain. Both clips stand on their own, but when viewed together, something magic happens. In the beginning of the scene Stallone wanders into, what appears to be, a very nice establishment.
By his gait, one would assume that he is literally drunk off bloodlust. He gets on the elevator, where he is confronted by Dr. Cox from Scrubs some other soon-to-be dead guy and an innocent old lady. While Cox rattles on about something, Stallone fantasizes about possible confrontations.
Just look at that asshole.
The real question is why, in his hypothetical imaginings, Carter ends up dying? Thankfully, the old woman's Stalloney sense begins tingling and she wisely exits the elevator at which point Carter springs his plan into action. His plan includes stabbing part of his hand into the sidekick's trachea, before clubbing the flamboyantly dressed Cox into submission ... with his fists. Stallone then exits the building looking relaxed as a man leaving a massage parlor ...
... and walks right into an ambush, making it clear that the mob knew that two men in an elevator would not be enough to slow down Jack Carter (and begging the question why they sent Dr. Cox in there in the first place). Stallone leads the bad guys in a roughly four-minute car chase during which his face communicates "nice Sunday drive" rather than "Holy shit-balls. They're trying to kill me!"