Tape one side of the box flaps shut. You will need to access the inside of the box, so leave the top open for now.
Hold up the fan to the outside of the box and trace the outline of it. Make sure that you trace the intake side of the fan.
Cut out the hole in the box. Mount the fan with screws and screwdriver onto the box so that the air will blow away from the box.
Cut a circle or square out of the opposite side of the box approximately 4 inches by 4 inches.
Cut two pieces of the air filter material about 6 inches by 6 inches wide. Attach one on the inside of the box with duct tape to cover the hole -- attach the other one with duct tape on the inside of the box to cover the intake of the fan. This will protect the housing of the fan from getting carbon particles in it.
Fill the box with the carbon. Spread it evenly throughout the inside of the box.
Tape the box shut. Make sure there are no holes.
Mount the box over the top of the hydroponic growing area, or install in front of the existing exhaust system with screws.