What is the strong lower part of the mantle located between the asthenosphere and the outer core?

The correct answer is the mesosphere. The mesosphere is the strong, lower part of the mantle that lies between the asthenosphere and the outer core. It is characterized by its rigidity and ability to withstand pressure, which differentiates it from the upper mantle's more ductile asthenosphere.

In this context, the asthenosphere is a semi-fluid layer that can flow over time and is situated above the mesosphere. The outer core, on the other hand, is composed of liquid iron and nickel and is found beneath the mantle, so it is not part of the mantle itself. The inner core is the solid center of the Earth, located beneath the outer core, while the lithosphere includes the crust and the uppermost portion of the mantle, which is relatively rigid. These distinctions help clarify why the mesosphere fits the description of the strong lower part of the mantle.