How can i have both hypothyroidism and hyperthyroidism?

Not at same time: Hyperthyroidism is an overactive thyroid, hypothyroidism is an underactive thyroid. You can't have both at the same time, but occasionally one can go from one to the other. The most common cause for both disorders is autoimmune thyroid disease. Depending on how the immune system is affecting your thyroid it can be over or underactive, or go from one to the other.