Final answer:
White blood cells digest bacteria using lysosomes, which contain digestive enzymes and acids that degrade the engulfed bacteria in a process called phagocytosis.
Step-by-step explanation:
The cell organelles directly responsible for the digestion of bacteria by white blood cells are lysosomes. During the process of phagocytosis, a white blood cell, such as a macrophage or neutrophil, engulfs the bacterium. This forms a vesicle known as a phagosome. The phagosome then fuses with a lysosome, creating a phagolysosome. Within the phagolysosome, the bacterium is exposed to digestive enzymes and acids that effectively kill and digest it. After the pathogen has been degraded, the leftovers are excreted from the cell through exocytosis, thus completing the process of phagocytosis.