Final answer:
The mode of genetic inheritance for the described disorder is X-linked recessive, specifically Duchenne muscular dystrophy.
Step-by-step explanation:
The mode of genetic inheritance for the disorder described in the case is X-linked recessive. The symptoms in the patient, such as muscle weakness, calf muscle enlargement, and a positive family history, are consistent with Duchenne muscular dystrophy (DMD), which is an X-linked recessive disorder. DMD primarily affects males and is caused by a mutation in a recessive gene on the X chromosome.