Gas stove venting

I bought a gas stove off craigslist and he gave me some venting pipe with it. The pope is interesting to me, it come out a 4" and empties into a 6". He said it gives out extra hear this way? It seems like a factory setup, but I'm new to gas stoves. Can I continue with 6" till I exit the house then step it to 4" with the adapter he have me? I'm adding a couple pictures if they will upload, so you can get the jis of what I'm talking about.

Sorry for all the gramatical errors! Cell phone autocorrect thinks it knows what I'm typing.

Yea I did its a dutchwest 28000 btu......The manual say for model# 2465,2466

If I can vent it right out the side of the house that would be nice. I wasn't sure how I would do that with the 6" off the top like that. Otherwise I was gonna vent up 6' then out the house then up another 16'.

By b vent you mean the adapter? The guy I bought it offer made it seem he was venting right out the side of the house. He said he gave me all his pipe minus the vent on the house, I just want to make sure it's safe.