What is the name of the earthen structure used to control water erosion and channel water flow?

The correct choice is the terrace, which refers to an earthen structure specifically designed to reduce soil erosion and manage water flow on sloped lands. Terraces are constructed as flat platforms or steps on hillsides, allowing rainwater to permeate the soil more effectively instead of running directly off the slope. This design minimizes erosion by slowing down water movement and promoting water retention, which is crucial for agricultural practices and sustainable land management.

While other options listed, such as a dam, levee, and ditch, also serve purposes related to water control, they do not fit the specific function of controlling water erosion in the same way that terraces do. A dam primarily stores water in a reservoir, a levee is built to prevent flooding by containing river flow, and a ditch serves as a drainage channel. These structures have distinct uses, making the terrace the best fit for the question regarding erosion control and water management on sloped terrain.