Which solution meets this requirement?

Explanations:

AWS Transit Gateway allows the connection of multiple VPCs and on-premises networks through a single gateway, enabling centralized management and simplifying network architecture. It supports both inter-VPC and VPC-to-on-premises connectivity.

AWS Direct Connect is a dedicated network connection that provides a private connection to AWS, but it does not inherently connect multiple VPCs; rather, it connects on-premises networks to AWS services. It can be used in conjunction with Transit Gateway but does not meet the requirement by itself.

VPC peering enables direct communication between two VPCs, but it does not support connecting multiple VPCs or on-premises networks through a single connection. Each peering relationship is one-to-one, requiring multiple connections for multiple VPCs.

AWS Client VPN provides a secure connection for individual clients to access AWS resources but does not connect multiple VPCs or on-premises networks through a single connection. It is more suited for remote access rather than interconnecting networks.