Explanation

Amazon EC2 instances (A) require operating system patching because:

• EC2 instances are virtual servers where customers have full control over the operating system
• Customers are responsible for patching the guest OS, security updates, and application software
• This falls under the AWS Shared Responsibility Model where customers manage the OS layer

Amazon RDS instances (D) require operating system patching because:

• While AWS manages the underlying infrastructure, customers are responsible for applying database engine patches and updates
• RDS instances run on managed infrastructure but still require periodic maintenance and patching
• Customers need to define patching windows and maintenance schedules

Why the other options are incorrect:

• AWS Lambda functions (B): Serverless functions where AWS manages the underlying infrastructure - no OS patching required
• AWS Fargate tasks (C): Serverless container platform where AWS manages the underlying infrastructure
• Amazon ECS instances (E): While ECS can run on EC2 instances, the question specifically mentions "Amazon ECS instances" which would typically refer to the managed service aspects

Note: The original image only showed Amazon EC2 instances as checked, but based on the question asking for TWO correct answers and the nature of AWS services requiring OS patching, both Amazon EC2 instances and Amazon RDS instances should be included in the document.