Facilitated diffusion is the process that does not use ATP. Unlike primary active transport, which requires ATP to move substances against their concentration gradient, facilitated diffusion is a passive transport mechanism that allows molecules to cross cell membranes with the help of transport proteins, moving down their concentration gradient without energy expenditure.
In receptor-mediated endocytosis and exocytosis, ATP is also required. Receptor-mediated endocytosis involves the internalization of substances into a cell, employing energy to form vesicles. Similarly, exocytosis requires energy to transport vesicles containing substances outside the cell. Therefore, among the options listed, facilitated diffusion is the only process that does not utilize ATP.