Compact layouts determine which key fields are displayed in a record's highlights panel, in the Salesforce mobile app, and on Kanban cards. To change the fields that appear on the Opportunity cards in the Kanban view, an administrator must modify the object's compact layout. The first four fields added to the compact layout are the ones that will be displayed on the Kanban card, providing a quick, at-a-glance summary of the record.

A. Record Type: Record Types control business processes, picklist values, and page layout assignments, but they do not directly define the fields displayed on a Kanban card.

C. Page Layout: Page layouts control the arrangement of fields, related lists, and other elements on a record's detail and edit pages, not the summary fields in the Kanban view.

D. Kanban Settings: Kanban settings are used to configure the columns (based on a grouping field like Stage) and the summarized metric (like Sum of Amount), not the individual fields on the cards.

1. Salesforce Help, "Compact Layouts": "A compact layout displays a record’s key fields at a glance in the Salesforce mobile app, Lightning Experience, and in the Outlook and Gmail integrations... In Lightning Experience, the first seven fields on a compact layout appear in an object’s record highlights panel and on Kanban cards."

Source: Salesforce Official Documentation. This directly links compact layouts to the fields displayed on Kanban cards.

2. Salesforce Help, "Customize the Fields that Appear on Kanban Cards": "The first four fields on an object’s compact layout appear on its Kanban cards. You can’t change the fields on Kanban cards from the Kanban settings menu. To change the fields that appear on Kanban cards, edit the object’s compact layout."

Source: Salesforce Official Documentation. This provides a specific procedural explanation confirming that the compact layout is the correct feature to modify.