How can a cloud administrator connect two cloud server instances privately on AWS without using an internet gateway?

Connecting two cloud server instances privately on AWS without using an internet gateway can effectively be achieved through a virtual private cloud (VPC) peering connection. VPC peering allows for a private network connection between two VPCs, enabling the instances to communicate with each other without traversing the public internet. This method ensures that the communication remains internal to the AWS infrastructure, providing a secure and efficient pathway for data exchanges.

Using VPC peering facilitates low-latency communication between the connected VPCs and allows for the sharing of resources, like databases and application servers, while maintaining security through private IP addressing. It is particularly beneficial for organizations managing multi-VPC architectures or when services are distributed across different AWS accounts.

While the other options presented can be used for various connectivity scenarios, they do not achieve the same outcome of private communication between instances without utilizing an internet gateway. A public IP address would expose instances to the internet, a VPN connection focuses on encrypting traffic for secure communication over public networks, and a Direct Connect connection provides a dedicated network connection from on-premises to AWS but does not directly facilitate instance-to-instance private communication without an internet gateway.