Bath fan duct replaced and insulated

My previous general contractor installed the housing for the bath fan I purchased. It’s designed for a 6″ duct. However, he connected it to the existing 4″ bath fan duct and used an adapter. The fan is capable of moving 110 cubic fee per minute, but the small duct is choking it. I decide to replace it with a new 6″ duct and a new 6″ vent on the outside of the house. I insulate the whole duct and connect it to the bath fan housing.

A bath fan housing with a large duct in the ceiling joists of a basement bathroom.