Amazon Aurora is the correct answer because it is a fully managed relational database that autoscales resources, and is compatible with both MySQL and PostgreSQL database engines. Aurora is designed to be fault-tolerant, self-healing, and to automatically scale storage and compute resources with minimal overhead or performance impact.

Amazon RDS also provides a managed relational database service but doesn't offer the same level of automatic scaling as Aurora does. Amazon DynamoDB, while fully managed, is a NoSQL database and does not provide relational database capabilities or direct compatibility with MySQL and PostgreSQL. Amazon Redshift is designed specifically for data warehousing and analytics, not for general purpose relational database workloads.