Which combination of AWS solutions will meet these requirements?

Explanations:

AWS Site-to-Site VPN provides a secure, encrypted connection over the Internet between the on-premises data center and AWS, using IPsec. This is essential for meeting the requirement of data encryption while also allowing for communication between the application server on AWS and the on-premises database.

AWS Direct Connect establishes a dedicated network connection from the on-premises data center to AWS. It reduces network latency compared to internet-based connections and can support IPsec encryption for secure data transfer, making it suitable for applications sensitive to latency.

AWS VPN CloudHub is primarily used for connecting multiple VPCs through VPN connections. While it does provide IPsec encryption, it is not applicable for the scenario described, as it focuses on inter-VPC connectivity rather than direct connectivity from on-premises data centers to AWS.

VPC peering is used to connect two VPCs within AWS, allowing resources in those VPCs to communicate. It does not facilitate a connection from an on-premises data center to AWS and therefore does not meet the requirement of securely connecting the legacy system to the database.

A NAT gateway allows instances in a private subnet to initiate outbound traffic to the Internet but does not establish a secure connection between on-premises data centers and AWS. It does not provide IPsec encryption or address the latency requirements of the database connection.