Comprehensive and Detailed 250 to 300 words of Explanation (AWS documentation-based, no links):

Routing requests to the “appropriate microservices” implies Layer 7 (HTTP/HTTPS) routing such as host-based or path-based rules (for example, /customers to one service and /orders to another). In EKS, the most direct and cost-efficient way to provide this style of routing is to use Kubernetes Ingress with the AWS Load Balancer Controller to provision an Application Load Balancer (ALB). An ALB natively supports HTTP/HTTPS request routing features (paths, hosts, headers), which map cleanly to microservices patterns and reduce the need for additional infrastructure components.

A Network Load Balancer (NLB) (Option A) is primarily Layer 4 and is best for TCP/UDP/TLS pass-through and ultra-high performance. It does not provide the same native HTTP path-based routing behavior required to steer requests between microservices based on URL structure, so it often forces you to add another routing layer (like an in-cluster ingress gateway), which can increase cost and operational complexity.

Option C is not an appropriate request routing mechanism; Lambda is compute, not an ingress/routing layer for EKS. Option D (API Gateway) can front services, but for simple microservice routing into EKS it typically adds per-request costs and additional configuration compared with using an ALB that is purpose-built for HTTP load balancing and routing. API Gateway is a great fit for API management features (throttling, usage plans, keys, transformations), but those are not requirements here.

Therefore, B is the most cost-effective and architecturally aligned solution for HTTP routing across EKS-hosted microservices using managed AWS-native ingress integration.