What are the words for the two parts of a round trip?

If you need to differentiate, they would be the outward leg and the return leg.

outbound |ˈaʊtˈˌbaʊnd| (adjective & adverb)
traveling away from a particular place, esp. on the first leg of a round trip: an outbound flight, flying outbound.

inbound |ˈɪnˈˌbaʊnd| (adjective & adverb)
traveling toward a particular place, esp. when returning to the original point of departure: inbound traffic, we have three enemy planes inbound on bearing two ninety.

Return is also adequate for the latter, as indicated by JeffSahol.

Parts of trips are legs, but that can also mean a trip where you had a layover (two legs in the same direction).

There are lots of additional options of interest here...

Though people do use the word legs, I think the more common thing in practice is actually going there and coming back as adverbial phrases (e.g., "Coming back, we fly Delta"); or you can simply talk about the outbound trip or outbound portion of the trip and the return portion of the trip ("The return portion of the trip is 6 hours long".)

You can even say "My/The return flight is 6 hours long." Since a return trip requires multiple flights, this is unlikely to cause ambiguity.

Finally, somebody mentioned the potential ambiguity of legs. Some of this ambiguity can be resolved by using segments instead (legs being made up of segments). This is a word that the airline folks tend to use a lot.