White blood cells are especially active when you are sick because their primary job is to fight off infections – often bacteria or viruses that do not belong in you. Once they locate the invader making you sick, they eat it and destroy it. What organelle do you think is plentiful in white blood cells?

Lysosomes

Explanation:

Lysosomes are membrane bound organelles that contain degradative enzymes. They degrade worn-out cellular parts and may also be used by cells to degrade/destroy invading bacteria or viruses. Hence, since white blood cells are primarily responsible for fighting infections, it is expected that they have a high amount of lysosomes (which they indeed do have in high amount).