The process by which plants absorb water from the soil through their roots is

Osmosis is the movement of water molecules from a region of higher water potential (dilute solution) to a region of lower water potential (concentrated solution) across a semi-permeable membrane. This is the primary process by which plant roots absorb water from the soil.

Soil water is a dilute solution with a higher water potential than the cell sap inside root hair cells, which contains dissolved mineral salts and sugars and therefore has a lower water potential. The cell membrane of the root hair cell acts as a semi-permeable membrane, allowing water molecules to pass through but restricting larger solute molecules. Because of this water potential gradient, water moves by osmosis from the soil into the root hair cells.

Diffusion is the movement of molecules from a region of higher concentration to one of lower concentration, but it applies to solute particles or gases moving down their own concentration gradient, not specifically to the net movement of water across a membrane. Transpiration is the loss of water vapour from the aerial parts of the plant (mainly through stomata) and, while it helps create the pull that draws water upward, it is not the mechanism of absorption at the roots. Photosynthesis is the process of converting light energy into chemical energy in the form of glucose and is unrelated to water uptake from the soil.

The correct process is osmosis, because it specifically describes the movement of water across the semi-permeable membrane of root cells driven by a water potential difference.