A 15 year old boy presents with acute onset of right flank pain, which developed after physical exercise. Physical examination demonstrates an area of ecchymosis in the right flank that is tender to palpation. The patient has a lifelong history of easy bruising. Sibling has same symptom. The serum level of clothing factor VIII is less than 2% of normal. Which of the following is the most likely underlying mechanism for bleeding tendency in this patient?