The question requires a solution for clients within the same VPC to resolve the IP address of a Compute Engine-hosted HTTP API. Option C is correct because it leverages Compute Engine's internal DNS, which dynamically resolves the instance's current internal IP address. This method is efficient and avoids unnecessary external traffic, making it the optimal choice for internal clients. Options A and B involve external IP addresses and load balancers, which are not necessary for internal communication within the same VPC. Option D does not provide a valid method for resolving the IP address of the service.