Which capability should the solutions architect use to meet the compliance requirements?

Explanations:

AWS Key Management Service (AWS KMS) is primarily used for managing encryption keys and does not facilitate network traffic routing between EC2 and S3. It does not address the requirement of ensuring that traffic does not traverse the public internet.

A VPC endpoint enables private connectivity between Amazon EC2 and Amazon S3 without the need for public IP addresses, ensuring that traffic remains within the AWS network and does not traverse the public internet. This solution meets the compliance requirement specified.

A private subnet ensures that instances launched within it do not have public IP addresses, but it does not automatically prevent traffic from going over the public internet for communication with S3 unless a VPC endpoint is specifically used.

A virtual private gateway is used for connecting a Virtual Private Cloud (VPC) to an external network, such as a VPN connection. While it helps in establishing secure connections, it does not directly prevent traffic from traversing the public internet for services like S3, thus not addressing the specific requirement.