I know there was to be an intake bringing in air or an exhaust moving out warm air. Why do people put carbon filters on the intake, it doesn't seem to make sense. Also, is it better to have the carbon filter on the inside of a grow box or the outside of the box on the exhaust fan?
You don't need a carbon filter on your intake. You might want some kind of filter to trap dust and keep bugs out, things like that, but you don't need to worry about drawing odors into the grow. There are different theories about placement on the exhaust. Ideally the best way is to pull through the filter (not push into the filter), so you fan needs to be "downstream" from the filter. Doesn't really matter if it's inside or outside the grow -- inside takes up space, which is fine if you have some to spare, and outside could be harder to hide.