The maximum covalency of oxygen is just 2 . However , it also shows other valencies like 1 in peroxides and 1/2 in superoxides .I suggest that you should reconsider your text. The reason is that oxygen is a member of period 2. It does not have a vacant d orbital hence no shifting of electron or excitation of electron takes place. On the other hand , yes ,various elements shows covalency of 4 like lead etc . Some elements even shows covalency of 7 like chlorine . This tendency generally decreases down the group due to inert pair effect .