An AABbccDdEeFF individual is crossed with an individual with the genotype AaBBCCDdEeff what is the probability that their offspring will have the genotype AaBBCcddEEFf?

Cross each allele separately to get the final genotype:

AA x Aa = AA, aa, Aa, Aa .: 1/2

Bb x BB = BB, BB, Bb, Bb .: 1/2

cc x CC = Cc .: 1

Dd x dd = DD, dd, Dd, Dd .: 1/2

Ee x Ee = EE, Ee, Ee, ee .: 1/4

FF x ff = Ff, Ff, Ff, Ff .: 1

Multiply all probable fractions:

1/2 x 1/2 x 1 x 1/2 x 1/4 x 1 = 1/64 chance of that specific genotype.