Explain how lysosomes inside a white blood cell might break down the particulates inhaled in the form of second hand smoke.

Lysosomes are parts of cells that perform the task of
breaking down dead cell components, food, and foreign matter including
microbes.

In the case you have mentioned, the particles
that have been inhaled have to be broken down by the lysosomes in the white blood cells.
This is done by fusing with the foreign particles and injecting enzymes that are
contained in the lysosomes.

Lysosomes contain over 40
different enzymes each of which helps to break down a particular type of organic matter.
For example lipids are digested by lipase, nucleic acids by nucleases,
etc.

The enzymes used to break down the particulates in the
smoke inhaled would depend on what the smoke consisted of. As lysosomes are equipped
with a large arsenal of enzymes they would be able to perform the task in an efficient
manner.