Which solution will meet these requirements with the LEAST amount of administrative effort?

Explanations:

VPC peering is limited in scalability, as it requires a separate peering connection for each pair of VPCs. This can become complex and difficult to manage with multiple VPCs across multiple Regions. Furthermore, it does not allow for transitive peering, which means communication between VPCs must be direct and manually managed.

AWS Direct Connect is primarily designed for connecting on-premises data centers to AWS. While Direct Connect gateways can help connect VPCs to on-premises networks, they do not provide a scalable solution for inter-VPC communication across multiple Regions. It involves more setup and management compared to other options.

AWS Transit Gateway allows for a hub-and-spoke model, simplifying the management of VPC communication. It enables the connection of multiple VPCs within a single Region and supports Transit Gateway peering to allow VPCs in different Regions to communicate with minimal administrative overhead, making it the most efficient solution for this scenario.

AWS PrivateLink is designed to provide secure access to services hosted in VPCs over the AWS network. It allows services in one VPC to be accessed from another VPC but does not facilitate broad inter-VPC communication across Regions like Transit Gateway does. It requires more management and may not scale as easily for multiple VPCs.