Which combination of steps should the solutions architect take to resolve this issue?

Explanations:

Deploying the database on a separate EC2 instance and creating a record set for its private IP in the private hosted zone would not resolve the issue, as the original problem is related to DNS resolution for the RDS endpoint in the private hosted zone. The database is still needed to be accessible via the existing CNAME record.

Manually adding the RDS endpoint IP address to the/etc/resolv.conffile on the EC2 instance does not address the core issue of DNS resolution through Route 53. Moreover, the/etc/resolv.conffile is not a reliable method for persistent DNS configuration and does not provide a scalable solution.

Creating an authorization to associate the private hosted zone in Account A with the new VPC in Account B allows the EC2 instances in Account B to resolve DNS queries against the private hosted zone in Account A. This is necessary for the application in Account B to resolve thedb.example.comCNAME record correctly.

Creating a private hosted zone for the example.com domain in Account B and configuring Route 53 replication is not necessary and would complicate the architecture. The existing private hosted zone in Account A should be used instead, as it already contains the needed DNS records.

Associating the new VPC in Account B with the hosted zone in Account A ensures that the VPC can resolve DNS queries from that hosted zone. This action will allow the application in Account B to properly resolve thedb.example.comCNAME record created in Account A.