Pinocytosis and phagocytosis occur in what part of the cell?

D) plasma membrane.

D. plasma membrane
Essentially, they are the same process, pinocytosis to take liquids, and phagocytosis to take solids, into a cell.  Outcroppings of the cell are produced to surround the particle.  The outcroppings meet and the sections of the membrane fuse.  That leaves the cell intact, with a vesicle, produced from portions of the cell membrane as its boundary.  

Often this occurs in single-celled animals.  The animal would use it to ingest food.  Once within the organism's (one cell) body, it would meet and fuse with digestive vesicles.  These vesicles contain digestive enzymes, which would break down the food particles, and the nutrients absorbed to the interior of the cell.  The remaining vesicle, with any indigestable bits and the enzymes would again fuse with the outer cell membrane.  The contents would be emptied to the outside, and the portions of the membranes of the vesicles would become part of the outer cell membrane again.  

Take a look at this cartoon of the process:
http://media-2.web.britannica.com/eb-media/78/22478-004-521EE704.gif