What should a solutions architect recommend to provide a highly available and scalable solution?

Explanations:

An internet-facing Network Load Balancer (NLB) can be used to register the on-premises static IP addresses, allowing it to distribute TCP traffic effectively across the on-premises servers. NLB is designed for high availability and can handle millions of requests per second while providing static IP addresses. It can route traffic to the registered IP addresses regardless of their location, making it suitable for hybrid architectures.

An internet-facing Application Load Balancer (ALB) is primarily used for HTTP and HTTPS traffic, operating at the application layer (Layer 7). While it can route traffic based on content, it is not optimized for TCP traffic distribution, making it less suitable for this scenario focused on distributing TCP traffic across on-premises servers.

Launching an Amazon EC2 instance with an Elastic IP address does not provide a scalable solution. While it can distribute traffic to the on-premises servers, it would require manual configuration and management of traffic, leading to a single point of failure and lack of high availability and scalability that a load balancer offers.

Launching an EC2 instance in an Auto Scaling group with public IP addresses would provide some level of scalability; however, it still relies on manual traffic distribution management and does not inherently distribute TCP traffic like a load balancer. Additionally, this option can also lead to a single point of failure without proper load balancing capabilities.