The correct answer is B, AWS Storage Gateway. This service acts as a bridge between on-premises applications and cloud-based storage, allowing for a hybrid storage solution. It caches frequently accessed data locally to provide low-latency access and ensures data durability by backing it up to Amazon S3 or Amazon Glacier. Option A, AWS Direct Connect, is incorrect as it provides a dedicated network connection rather than storage solutions. Option C, Amazon S3, is an object storage service but does not offer the local caching feature required by the question. Option D, AWS Snowball Edge, is a data transfer device and not a service that connects on-premises applications to cloud-based storage with local caching.