Which tactical mission task requires the complete elimination of enemy forces within a designated area?

The tactical mission task that requires the complete elimination of enemy forces within a designated area is referred to as "Clear." This task involves not only engaging and destroying enemy forces but also ensuring that the designated area is free of adversaries and safe for friendly forces to operate. Clearing an area is critical in many military operations, particularly in scenarios where establishing control and safety for subsequent operations is a priority.

In contrast, "Destroy" refers to the action of rendering enemy forces or capabilities ineffective, but it does not specifically imply the complete elimination from a designated area. Destroying might involve crippling an enemy's ability to fight without necessarily involving ground control of the area.

"Close Air Support" focuses on providing air strikes in support of ground troops, dealing primarily with fire support rather than the ground task of clearing an area of enemy presence.

"Contain" involves restricting the movement of enemy forces, rather than eliminating them from an area. The goal of containment is to prevent enemy forces from expanding into other areas or regrouping, but it does not eliminate them or clear the area.

The specificity and thoroughness of the "Clear" task make it the correct choice for indicating the complete elimination of enemy forces within a designated area.