Which region of a neuron is considered the "biosynthetic center of a neuron" as it contains a large quantity of rough endoplasmic reticulum involved with protein synthesis?

It is in the Cell body. The Cell body, likewise called the soma, is the round piece of the neuron that contains the core. The phone body interfaces with the dendrites, which convey data to the neuron, and the axon, which sends data to different neurons.