The requirement for the new division's network team to have 'complete control over their networking infrastructure' while allowing communication between divisions and avoiding unnecessary permissions points directly to VPC Network Peering. This approach allows each division to manage its own VPC independently (in its own project), provides full control to the new division's network team within their project, and enables secure, private communication between the VPCs without traversing the public internet. Granting roles/compute.networkAdmin on their newly created project ensures they have the necessary control over their dedicated VPC. Using Shared VPC (option D) would centralize network administration under your existing project, which goes against the requirement of the new division having 'complete control.' VPN (option C) would incur additional costs and introduce more complexity than VPC peering for intra-Google Cloud connectivity. Option B is flawed because creating a subnet in the new VPC isn't directly relevant to granting permissions on the new project for VPC peering setup, and networkuser role on the new project alone wouldn't give complete network control.

Exact Extract:

'VPC Network Peering allows you to connect two VPC networks so that resources in each network can communicate with each other using internal IP addresses. Traffic stays within Google's network.'

'Each side of a VPC Network Peering connection is configured independently. This means that each network administrator retains full control over their own network, including routes, firewalls, and network services.'