Question

Which earth sphere causes the erosion of soils by running water such as rivers and oceans

Answer 1

Well you know it's not something like geosphere because its main job is to regulate the movement of Earth's crustal layers by rebuilding and destroying them.

Atmosphere is out of the question too because its job is to protect us from solar radiation and small-scale meteors.

Biosphere just involves the organisms and environment around us.

What does that leave you with? Cryosphere and Hydrosphere. I think you can figure it out from there :)