Flow Builder is the appropriate declarative automation tool for this requirement. An administrator can create a schedule-triggered flow that runs at specified intervals. This flow can be configured to find records that meet specific criteria based on their field values and then use the "Delete Records" element to automatically delete them. This solution is fully automated and does not require manual intervention after its initial setup, directly addressing the administrator's need for an automated way to delete records based on field values.

B. Automation Studio: This is a component of Salesforce Marketing Cloud used for marketing automation tasks, not for general record management on the core Salesforce platform.

C. Mass Delete Records: This is a manual tool found in Setup. While it allows deleting records based on criteria, it requires an administrator to initiate the process each time and is not an automated solution.

D. Flow Orchestration: This tool is designed to coordinate complex, multi-step, and multi-user business processes. Using it for a simple conditional record deletion would be unnecessarily complex; Flow Builder is the more direct and suitable tool.

1. Salesforce Help - Flow Builder: "Flow Builder is the declarative interface used to build individual flows. You can use Flow Builder to build code-like logic without using a programming language." This establishes Flow Builder as the primary tool for declarative process automation.

Source: Salesforce Help, Flow Builder, Article 000388393.

2. Salesforce Help - Flow Element: Delete Records: "To delete Salesforce records that you’ve stored in a record variable or a record collection variable, use the Delete Records element... To find Salesforce records to delete, use the Get Records element." This confirms the capability of a flow to find and delete records.

Source: Salesforce Help, Flow Element: Delete Records, Article 000386220.

3. Salesforce Help - Schedule-Triggered Flow: "A schedule-triggered flow starts at a specified time and frequency for a batch of records... Create a schedule-triggered flow that runs on a recurring schedule for a batch of records." This document confirms the automation capability required by the question.

Source: Salesforce Help, Schedule-Triggered Flow, Article 000383271.

4. Salesforce Help - Mass Delete Records: "You can mass delete accounts, leads, activities, contacts, cases, solutions, products, and reports... From Setup, in the Quick Find box, enter Mass Delete Records, then select Mass Delete Records." This documentation describes a manual setup tool, contrasting with the "automated way" required.

Source: Salesforce Help, Mass Delete Records, Article 000383279.