Step 1: Recall what clathrin is.
Clathrin is a three legged, triskelion shaped protein that assembles into a lattice on the inner face of the plasma membrane. This lattice pulls the membrane inward, forming what is called a clathrin coated pit.
Step 2: Follow the pit through to a vesicle.
Once the pit is deep enough, the protein dynamin pinches its neck, releasing a clathrin coated vesicle into the cytoplasm carrying whatever was bound at the membrane surface.
Step 3: Attach this to a real process.
This exact pathway is how a cell performs receptor mediated endocytosis. Surface receptors, such as the LDL receptor for cholesterol uptake or the transferrin receptor for iron uptake, cluster together after binding their ligand, gather inside a clathrin coated pit, and get pulled into the cell as a coated vesicle.
Step 4: Rule out the remaining options.
Endocytosis that does not depend on a specific receptor, like bulk fluid phase uptake or caveolae mediated uptake, generally runs through clathrin independent routes, not this pathway. Exocytosis, whether receptor mediated or not, is the release of vesicle contents out of the cell and is driven mainly by SNARE proteins docking and fusing the vesicle with the membrane, not by clathrin coats.
Step 5: Final answer.
Clathrin is involved in
\[ \boxed{\text{Receptor mediated endocytosis}} \]