What command relationship gives the authority to organize and employ forces and assign tasks?

The command relationship that provides the authority to organize and employ forces as well as assign tasks is operational control. This type of control allows a commander to direct forces as necessary to execute missions or tasks while also having the flexibility to make adjustments to the organization of forces, the allocation of resources, and the assignment of specific tasks.

Operational control is essential in joint operations where forces from different services or nations may need to work together efficiently. It enables commanders to align various units toward a common operational goal while still allowing for tactical flexibility and adaptability on the battlefield.

In contrast, the other options refer to different aspects of command but do not convey the same breadth of authority. For instance, organic pertains to forces that are inherently a part of a unit, assigned refers more to specific tasks delegated to a unit, and coordinate implies working together but without the authority to direct forces or make changes in organization or task assignment.