Using P for the allele for polydactyly and p for the allele for the normal number of digits. Since Joan's mom has polydactyly, but only some of her children got this dominant allele, Joan's mom is Pp. Her unaffected father must be pp since not all of the children have the trait. That makes the cross between her parents ppxPp, and Joan could only have one copy of the P allele, making her Pp.
Work Step by Step
This is asking you to do pedigree analysis on Joan's family. Pay special attention to the dominant nature of polydactyly to see that her father must be homozygous recessive (as it's the only way he would not exhibit polydactylism) and that her mother must be a heterozygote for any siblings to also be unaffected/have a pp genotype. Then you can see that Joan, who must be NN or Nn to have the trait, could not be NN from these parents, making her Nn.