The cell membrane is permeably selective, and some solutes cannot freely diffuse across this membrane. What is the name of the process wherein a solute is transported across a membrane by a protein from a region of high solute concentration to a region of low solute concentration without any needed input of energy?

Facilitated diffusion (passive transport)

Explanation:

The plasma membrane is selectively permeable as it allows the selected molecules to freely pass through itself but the molecules which are not passed require special proteins. The transport through these proteins may or may not require energy which depends on the concentration gradient in which the process which requires energy is called active transport and which do not is called passive transport.

The movement of molecules from higher concentration to lower concentration takes place by diffusion but there are some molecules that do not easily pass through the membrane and require proteins is known as facilitated diffusion.

Thus, facilitated diffusion is correct.