Step 1: A tall young man with an early diastolic murmur points to aortic regurgitation from aortic root dilatation, classically seen in Marfan syndrome (a fibrillin-1 connective tissue disorder).
Step 2: Read the pedigree. The trait appears in every generation, affects males and females equally, and there is at least one instance of male-to-male (father-to-son) transmission. That combination rules out X-linked inheritance and recessive patterns.
Step 3: Vertical transmission through every generation with an affected parent passing the trait to roughly half the children is the hallmark of autosomal dominant (AD) inheritance. The mutated gene expresses itself in the heterozygous state, and AD disorders typically affect structural or non-enzyme proteins (here, fibrillin), with variable expressivity and reduced penetrance.
So the inheritance is AD.
Ref: Robbins Basic Pathology, 9e.