We could break down the sentence and maybe make it clearer like this:
Traffic congestion wastes fuel.
This makes more carbon dioxide, by means of the car exhaust.
So it contributes to the greenhouse effect.
The verbs in the sentence are wastes, produces, and contributes.
I think the sentence is a little hard to understand because exhausts is not a verb in this context; it means "the escape of used gas or vapor from an engine" or "the conduit through which used gases escape". So it's not "through the car", but through the car exhaust.
The sentence is not very clearly written. I would not have written "produces more carbon dioxide through the car exhausts" but "produces more carbon dioxide in car exhaust", because "the car exhausts" is not very idiomatic. There's no reason to say the car exhausts, because we're not talking about specific cars or specific exhausts, and there's not reason to say exhausts, because we're talking about exhaust as a general phenomenon.