Within a pedigree, only males exhibit a trait of interest and the trait commonly passes from a male to his grandsons through his daughters and never through his sons. What is the most likely mode of inheritance, assuming complete penetrance?

X-linked/Sex-linked recessive inheritance

Explanation:

The most likely mode of inheritance of the trait is an X-linked recessive inheritance.

The sex chromosome of a male is XY while that of a female is XX. The Y chromosome is hypothesized not to carry any allele ordinarily. Hence, a male child only needs to inherit one affected allele to become affected for recessive X-linked traits.

During gamete formation, the sex chromosome of the male segregates into X and Y gametes while that of the female segregates into X and X gametes. During fertilization, the X gamete of the male is usually inherited by the female while one of the X gametes of the female is usually inherited by the male.

Assuming a father is affected for an X-linked recessive trait, the affected X chromosome will be passed to a female child and such a child would be a carrier, rather than being affected since she requires the two X chromosomes to be affected in order to exhibit the trait.

The affected X chromosome is thus passed to her male child according to the law of inheritance of the sex chromosome. Hence, the grandson of the affected man inherits the trait through the daughter of the affected man.

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hope this you! : )

(i popped my answer into google translate so it may be a bit wonky)