The only process shown in Figure 9-3 that does not use a cell's energy is D. Diffusion.
Diffusion is the movement of molecules from an area of high concentration to an area of low concentration without the use of energy.
The other processes shown in Figure 9-3 all require energy from the cell:
A. Active transport: The movement of molecules against their concentration gradient, which requires energy.
B. Osmosis: The movement of water across a semipermeable membrane from an area of high water concentration to an area of low water concentration. Osmosis requires energy because the cell needs to use energy to maintain the concentration gradient between the inside and outside of the cell.
C. Exocytosis: The process by which cells release molecules to the outside of the cell. Exocytosis requires energy because the cell needs to use energy to move the molecules to the cell membrane and then to fuse the membrane with the vesicle containing the molecules.
Therefore, the answer is D. Diffusion.