An example of vesicle-mediated transport would be:

diffusion of oxygen

diffusion of lipid-soluble molecules across the membrane

the actions of the sodium-potassium pump

cell secretion by exocytosis

An example of vesiscle-mediated transport would be cell secretion by exocytosis.

The reason why this would be an example of vesicle-mediated transport is because all the other types of transport listed here are not something you would call vesicle-transport; the substances don't really get transported in vesicles. This is different in exocytosis where the compounds gets packaged into vesicles.