Explanation

VPC peering is the correct answer because:

• VPC peering allows you to connect two VPCs together, enabling them to communicate as if they were in the same network
• Inter-Region VPC peering specifically supports connecting VPCs across different AWS Regions
• It uses the existing VPC infrastructure without requiring additional hardware or complex configurations
• It provides private connectivity between VPCs using AWS's backbone network

Why the other options are incorrect:

• AWS Client VPN: This is used to provide remote access to AWS resources for individual users, not for connecting VPCs
• AWS Direct Connect: This establishes a dedicated network connection from on-premises to AWS, not between VPCs in different regions
• VPC endpoints: These provide private connectivity to AWS services, not for connecting two VPCs together

VPC peering is the most appropriate solution for establishing a direct, private connection between VPCs in different AWS regions while leveraging existing infrastructure.