I have an avulsion of the distal fibula fracture due to a high ankle sprain. what is the the common treatment for this type of injury?

Depends: If the fracture is displaced it may need surgical fixation. If its not displaced then bracing for 6-8 weeks minimum and then return to rehab until fully healed. It can take several month to get full healing. Other options include possible platelet or stem cell based therapies that may help healing faster/more fully. Check out Regenexx.Com.