Which combination of architectural changes will reduce the NAT gateway costs?

Explanations:

Configuring a VPC peering connection allows instances in the client VPC to communicate with the API in the other VPC using private IP addresses, thus avoiding the need for the NAT gateway, which would be used for public internet access. This reduces costs associated with NAT gateway data processing.

AWS Direct Connect provides a dedicated network connection between on-premises networks and AWS, but it does not directly connect VPCs. It would not be effective for reducing NAT gateway costs between two VPCs.

ClassicLink allows EC2-Classic instances to communicate with instances in a VPC, but it is limited to EC2-Classic environments and does not provide a way to connect VPCs or reduce NAT costs. This option is not applicable for VPC-to-VPC communication.

Configuring a PrivateLink connection allows secure communication between VPCs using private IP addresses. This enables the client application to access the API without going through the NAT gateway, thus reducing costs.

AWS Resource Access Manager (RAM) enables resource sharing across accounts, but it does not directly facilitate network connectivity between VPCs. Therefore, it does not help in reducing NAT gateway costs in this context.