River erosion is the process by which water wears away the land. It is affected by several factors, including the depth, breadth, flow, and gradient of the river. Option 1 suggests that river erosion is highest where the depth of the river is more. While depth can contribute to erosion, it is not the main factor. Option 2 suggests that river erosion is highest where the breadth of the river is more. Similar to option 1, breadth can contribute to erosion, but it is not the primary factor. Option 3 states that river erosion is at its greatest where the flow is fast. This is the correct answer because a fast-flowing river has more energy to carry and transport sediments, leading to increased erosion. Option 4 suggests that river erosion is highest where the gradient is more. While gradient can affect erosion, it is not the main factor.

Therefore, the correct answer is option 3.