Which type of enlargement allows a tapered fastener to be flush with the material's surface?

The type of enlargement that allows a tapered fastener to sit flush with the surface of a material is called a countersink. Countersinking involves creating a conical hole in the material that matches the angle of the fastener's head, which is typically tapered. This design not only allows the fastener to be recessed into the surface, providing a smooth, even finish, but it also helps reduce the risk of snagging and protects the fastener from damage.

In contrast, counterboring creates a cylindrical hole that allows the fastener to sit flat but does not accommodate the tapered shape of the fastener's head. Therefore, it does not provide the same flush finish as countersinking. The other two options, Degrees of Freedom and Data Panel, are unrelated to fastening techniques, focusing instead on concepts in mechanics and user interface elements respectively. Therefore, countersinking is the correct choice for achieving a flush finish with tapered fasteners.