1/2" soundboard and 1/2" MDF. For a 6" 440cfm fan you will need to cut the pieces around 30" square. Screw soundboard onto mdf and screw all together to make a box with soundboard inside. Cut out flange holes and install flanges on outside for ducting. Put fan in and sync down. Put lid on. Always, always, yes always use insulated duct. R6 works great R8 is better. Fire it up. You will drop about 90% of the noise. Wrap the box in panda film if they sit inside the room.
I have a little 4" exhaust fan in a hole in the ceiling. The hole was cut about a half inch bigger all around than it needed to be for the fan. I insulated the fan all around with soft foam rubber. This made it much quieter, eliminating the solid contact with the ceiling board, which was amplifying the sound of the fan. Hope this helps.