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

Explanations:

This option suggests deploying the database on a separate EC2 instance and creating a record set for its private IP, which doesn’t address the issue of DNS resolution from the EC2 instance in Account B. The original goal is to resolve db.example.com, which is already set up in the private hosted zone in Account A.

Manually adding an RDS endpoint IP address to the /etc/resolv.conf file does not resolve the underlying issue of DNS resolution and is not a sustainable or recommended solution. Changes to /etc/resolv.conf may not persist and do not solve the problem of inter-account DNS resolution.

Creating an authorization to associate the private hosted zone in Account A with the new VPC in Account B allows resources in Account B to resolve DNS records in the private hosted zone of Account A. This step is essential for enabling cross-account DNS resolution.

Creating a private hosted zone in Account B and configuring Route 53 replication is unnecessary and does not resolve the existing DNS resolution issue. The focus should be on enabling access to the already established private hosted zone in Account A.

Associating the new VPC in Account B with the hosted zone in Account A allows the EC2 instances in Account B to resolve DNS records defined in the private hosted zone in Account A. This step directly addresses the problem of DNS resolution.