Final answer:
The transition from brittle to ductile failure occurs at the asthenosphere, which is below the lithosphere and where mantle material behaves plastically.
Step-by-step explanation:
The depth at which the transition from brittle to ductile failure occurs is typically at the boundary between the lithosphere and the asthenosphere. The lithosphere is composed of the crust and part of the upper mantle and it behaves as a brittle, rigid solid. This is where earthquakes happen, as the rocks break due to stress. In contrast, the asthenosphere underneath is partially molten and behaves plastically, meaning it can flow without fracturing, which represents the ductile behavior of rocks. Therefore, the correct answer is B. Asthenosphere, as it is the region where the behavior of mantle material changes from brittle to ductile.