To achieve multi-Region high availability for a serverless API-based application, the architecture must be duplicated in the second Region and supported by a multi-Region data layer and appropriate DNS routing. Option A provides the required multi-Region data layer using DynamoDB global tables, which replicate data automatically and asynchronously between Regions. This allows reads and writes in either Region and prevents cross-Region latency bottlenecks.

Option C ensures that the compute components—API Gateway REST API and AWS Lambda functions—are deployed in both Regions. Each Region operates independently, providing true active-active redundancy and allowing Route 53 to route traffic directly to either Region without dependency on the other.

Option E selects Route 53 latency-based routing, which directs each user to the Region with the lowest round-trip latency. This meets the requirement to route traffic based on the Region providing the best response time rather than only providing active-passive failover.

Option D (failover routing) supports active-standby topologies, not active-active. Option B creates a global secondary index, which does not provide multi-Region replication. Option F (multivalue routing) distributes traffic randomly and does not account for latency or Region placement.

Thus, combining DynamoDB global tables, duplicated serverless architecture, and latency-based routing fully satisfies the requirements.