The solution that the app builder should use to meet DreamHouse Realty's needs is Master-Detail Child Object. A master-detail relationship can be used to create a parent-child relationship between two objects, where the child records inherit the sharing and security settings of their parent record. The app builder can create a roll-up summary field on the parent object to calculate the highest value of all child records. Option B is incorrect because Text Area (Long) is a field type that allows users to enter up to 131,072 characters on one line, which is not suitable for this requirement. Option C is incorrect because Multi-select Picklist is a field type that allows users to select multiple values from a predefined list, which is not suitable for this requirement. Option D is incorrect because Lookup Object is not a valid term, but rather Lookup Relationship, which is a type of relationship that links two objects together, but does not support roll-up summary fields.

The app builder should create a sharing rule that grants the users Read/Write access to the Application records. A sharing rule is a type of rule that can extend record access to groups of users based on certain criteria. In this case, the app builder can create a sharing rule that grants Read/Write access to the Application object to the recruiters based on their role, public group, or queue. This will allow them to edit the Application records related to any Internship record, regardless of the ownership. Option A, B, and C are not ways to configure the proper access.