What causes high white blood count along with high absolute monocytes levels show?

Infection. Elevated WBC count is usually a response to an infection. The elevated monocytes may mean that you have a chronic infection or an autoimmune condition. You are taking methylprednisolone which is also used to treat the symptoms of an autoimmune condition so the elevated monocytes may be due to the condition that you are taken that med for. Check with your doctor.