Explain why a flame from a bunsen burner will not pass through a piece of metal (wire) gauze for quite some time.

When the wire gauze is held over a flame, the gauze conducts a lot of heat from the flame.
So, the gas reaching above the gauze fails to acquire its ignition temperature and therefore it does not burn above the wire gauze.
After a sufficient time has passed, the temperature above the gauze will become equal to ignition temperature. Thus, at this temperature, the gas will burn and the flame will appear.