What does Gatsby reply when Nick asks him how he makes his money in The Great Gatsby?
In addition to the great response above, it is good to add that this particular point in the novel is one of personal victory to Gatsby. He is there with Daisy, and he is about to show her around his house. Showing off how "well" he has done for himself means, to Gatsby, that he is finally worthy of Daisy. Having Nick there serves as further proof to Gatsby that he is distinguished and admired by many.
However, in the conversation that ensues as Daisy goes to wash her face, we notice that there are cracks in Gatsby's surface that reach straight to the core of his insecurities and his feelings of worthlessness. After all, Gatsby is not about who he is, but what he has.
"The house looks well, doesn't it?" he [Gatsby] demanded. "See how the whole front of it catches the light."
I agreed that it was splendid.
"Yes." His eyes went over it, every arched door and square tower. "It took me just three years to earn the money that bought it."
"I thought you inherited your money."
At this point, Gatsby gets nervous realizing that he has been caught in a lie, a type of lie that would push him quite low in the social ranking of the peers that he is desperately trying to impress. The society that Gatsby wants to dominate is one where everything is given for no reason. They are idle heirs and heiresses with not a worry in the world who have never had to work for a living. To that society, working for a living is something done by the poor by birth—hence, their feelings of entitlement and debauchery with the money and all the many things they inherit just for being who they are. Gatsby does not share this origin, and it gnaws at him inside. This is why the next exchange makes Gatsby more guarded still.
"I did, old sport," he said automatically, "but I lost most of it in the big panic -- the panic of the war."
I think he hardly knew what he was saying, for when I asked him what business he was in he answered, "That's my affair," before he realized that it wasn't the appropriate reply.
After telling Nick off, basically, Gatsby immediately tries to gain ground by retracting his reply and adding that "he has been many different things." This is evidence of Gatsby's inner fears of his origins and his background—and also of the fact that he knows he is deceiving others as well as himself.
Quite simply, Gatsby replies with a tart, "That's my affair." Oh my, Gatsby gives throws a pretty quick barb at Nick in the middle of Chapter V when he asks Gatsby that question, doesn't he? Let's look at the entire exchange:
I think he hardly knew what he was saying, for when I asked him what business he was in he answered: "That's my affair," before he realized that it wasn't an appropriate reply.
"Oh I've been in several things," he corrected himself. "I was in the drug business and then I was in the oil business. But I'm not in either one now."
Gatsby's reaction is incredibly telling. It reeks of anxiety and gives wonderful evidence (and some of the first we are presented with) that Gatsby is doing something that is not entirely legal, ... or at least something that is not entirely accepted by mainstream society.
The exchange also provides another example of the awkwardness of Gatsby's personality in personal discourse. Just as Gatsby is out of place (even in West Egg), he is even out of place in everyday pleasantries.