Carbon filters, exhaust fans and air tubes need all to be properly connected, forming a sort of ventilation system in order to work seamlessly.
If all of the pieces are of the same size (diameter), all you need to do is binding them - this could be done by the metal tie or cable ties reinforced by strong, wide insulation tape.
When one or more devices are different from the rest, you should look for a reduction.
This round piece of plastic or metal can be attached in between the two appliances that don't fit one another - e.g. a 125/150 reduction will allow you to connect a 150mm air pipe to the 125mm fan.
If you are using a single speed exhaust fan with no external sensors, you might also consider using separate controllers.
Those devices are designed to give you full control over your whole ventilation system.
Ranging from the simple manual speed regulation to temperature, humidity, negative pressure and histeresis regulation enabled ones, they have something to offer for both amateurs and advanced growers.