A Roll-Up Summary field is the correct solution because it is specifically designed to calculate values from related detail records and display them on the master record. In a master-detail relationship, this field type can be created on the master object (Shoec) to automatically count the number of related detail records (Subscriptionc). This directly addresses the requirement to track how many subscriptions have been sold for each shoe catalog without needing custom automation.

B. Lookup field: A lookup field is used to create a relationship between objects, not to aggregate or count related records.

C. Master-detail relationship field: This field type establishes the master-detail relationship itself. The question states this relationship already exists; the goal is to summarize data, not create the link.

D. Number field: A standard number field would require manual data entry or custom automation (like a Flow or Apex trigger) to keep the count updated, making it less efficient than the declarative Roll-Up Summary field.

1. Salesforce Help Documentation: Roll-Up Summary Field. This document states, "A roll-up summary field calculates values from related records... You can create a roll-up summary field to display a value in a master record based on the values of fields in a detail record. The detail record must be on the detail side of a master-detail relationship with the master record." It explicitly lists COUNT as a possible calculation.

2. Trailhead by Salesforce: Data Modeling Module, Create Object Relationships Unit. In the section "Master-Detail Relationships," it explains, "This relationship allows you to create roll-up summary fields. Roll-up summary fields are super useful. They allow you to calculate the sum, average, or count of detail records." This confirms that the master-detail relationship is a prerequisite for using a roll-up summary to count records.

3. Salesforce Object Reference for Salesforce and Lightning Platform: Standard and Custom Objects. In the section on "Relationships Among Objects," it details that only master-detail relationships support roll-up summary fields, which aggregate data from child records.