Well, you can suck through a carbon filter, or you can blow through one. If you suck through one, it should be something like this order:

outside air -> inside cabinet -> carbon filter -> tube -> fan -> exhaust

You could swap the positions of the tube and the fan here and not really affect anything. On my carbon filter at least, the air doesn't just come in or go out the holes at the ends, but along the entire length of the filter. And therefore, sucking air through it would have basically mandated that it be INSIDE the cabinet, and it's too big to waste that much precious grow space inside the cabinet.

To blow through it, the filter should be outside the cabinet, in my opinion, as again, it blows out (clean) air all along the length of the filter, and clean air outside the cabinet is exactly what you want. In this configuration, it should be something like:

outside air -> inside cabinet -> tube -> fan -> carbon filter

You could shift the tube and the fan around here in their position if you wanted to, and it'd work the same. I used standard 6" ducting and duct connectors to attach the filter (which itself came with a 6" duct flange).

Those inline fans can't handle static pressure (e.g., generate suction or blow against resistance), so they aren't really useful for blowing or sucking through a carbon filter. The blades would just slow to a crawl and eventually fry the motor, and you'd get little air movement or filtering even before it died. Centrifugal fans are the best, then squirrel cage fans, then axial/inline/computer fans. Lighting should always be the first concern, but I think fans should be a close second; you get what you pay for, pretty much.