Dominant traits show their phenotype, and you see that 1 (the father) exhibits the trait. Male= XY. Female in I is a carrier (heterozygous) because 6 in II is heterozygous to produce a daughter that shows the trait (6 is homozygous recessive).
All the sons are affected in I, so if it's sex linkage, it means that the mother is a carrier (heterozygous). Notice how only the females are unaffected in II? 2 and 4 don't show the trait? So it ONLY AFFECTS THE MALE IN I.
And then looking at III, you see that 2 is a female and has the trait? It means that 4 in II is a carrier. For a female to exhibit a trait, she must be homozygous to exhibit the symptom. Sex linkage usually occurs on the X chromosome, so I have no idea why 4 in III doesn't show the trait. If you think about it, his mother has the trait in both her alleles (otherwise she wouldn't exhibit the phenotype) and the father has both the alleles too (otherwise 3 in iI wouldn't show the trait).
I don't think it's sex linkage.