When the cell engulfs large fragments of matter, it is called
endocytosis
exocytosis
pinocytosis
phagocytosis

The answer is phagocytosis.

Phagocytosis is process in which cell engulfs large fragments of matter, for example, bacteria, mineral particles, dead cells. These fragments form a phagosome which fuses with lysosome and form a phagolysosome. Inside the phagolysosome, enzymes and toxins break down those fragments.

Phagocytosis is actually a specific form of endocytosis. Endocytosis is process in which cell engulfs molecules, such as proteins. Pinocytosis is fluid endocytosis. Exocytosis is the opposite process to endocytosis. In exocytosis cell transport molecules, such as proteins, out of cell.