Hardness is a property of a material that determines its ability to ______.

Hardness is defined as a material's resistance to localized plastic deformation, which often manifests as the ability to withstand scratching, indentation, or abrasion. In the context of this question, the correct answer highlights that a harder material can effectively cut or scratch softer materials, including other metals. This property is crucial in many applications such as machining and cutting tools, where the hardness of the cutting tool must exceed that of the material it is intended to cut to ensure efficiency and effectiveness.

The concept of hardness allows for the selection of appropriate materials for specific tasks. For instance, cutting tools made from harder materials can maintain sharper edges longer and achieve better performance when machining or shaping softer metals.

In contrast, the other options describe properties related to other mechanical characteristics of materials, like their ductility or malleability. These properties do not directly pertain to how well a material can cut or be used in cutting applications. Thus, while those characteristics are important in their own right, they are not the defining factor in relation to the property of hardness.