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.  

readability="15">

"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. 

readability="15">

"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.