The correct answer to this open question is the following.
The waterway that you would traverse (travel along) in order to trade from Mogadishu to Quanzhou is the Shebelle River located in Somalia, Africa.
The Shebelle River runs from the mountains of Ethiopia, in the region known as the "horn" for the shape of this part of the African continent, to Somalia. It runs through the capital city of Somalia, Mogadishu. It is an important river that has served the people from the region to transport people, goods, and raw materials, that increased trade in the region.