Which type of transport does not require energy in moving proteins around the cell?

Passive transport is the correct answer because it describes the movement of proteins or other molecules across a cell membrane without the expenditure of energy. This process is driven by the concentration gradient, where molecules move from an area of higher concentration to an area of lower concentration, thereby naturally equilibrating concentrations within the cell.

In contrast, active transport involves the movement of molecules against their concentration gradient, which requires energy typically derived from ATP. Facilitated diffusion is a specific type of passive transport that involves transport proteins helping move substances across the membrane, but it still does not require energy. Endocytosis, which involves the engulfing of materials into the cell, is another active process requiring energy. Therefore, passive transport is highlighted as the method of moving proteins that does not require energy, showcasing the cell's ability to utilize natural gradients to facilitate molecular movement efficiently.