Basics of cooling + odor control

We all know the way to do this is with ducts + carbon filters. My question here is how this should optimumly?

Could someone explain to me how the carbon filter+ inline fan combo works? Are you just sucking air then pushing it through the carbon filter releasing clean air? Or are you sucking from the carbon filter then outputting clean air into the room. Wouldn't this be the same? If anyone could show their set ups that would be killer!

Just here to learn! any help would be appreciated!

You have a blower that is connected to your grow room that is sucking in fresh air from a source, like another room or the outside. At the same time it's sucking in fresh air, it's blowing it into your grow room.
Then you'll have a carbon filter somewhere on the other side of the room that is connected to another blower. This blower will be sucking the stale air through the carbon filter. The carbon inside the filter, filters the stale air and then is blown through the blower to another area like a chimney or something that leads to the outside.
While both of these blowers are working you should be exchanging the stale air with fresh air 1-2 times a minute. Also inside the grow room you'll have an oscillating fan moving all of the fresh air everywhere inside your grow area.
I would have to say that this part of grow is the most critical to setup properly. Mostly due to the fact that you have to keep humidity and temperature consistant. But at the same time you need to exchange the air 1-2 times a minute.

100% agreed with Bongjuice! i learned this the hard way after my leafs strted curling and the heat got awful...so stale...but now fixed!

Could you show me an example of a set up and the types of blowers?