Dear student, The no. of voids = octahedral voids + tetrahedral voids
=>No.of octahedral voids in one mole of gold is= Avagadro no.x1 (since no of octahedral voids are equal to no.of unp atoms present in the sample )
=>No.of of tetrahedral voids in one mole of gold is= Avagadro no. x2(since the no. of octahedral voids is twice the no. of of atoms present in the sample)
Therefore, The total no. Of voids is=1*avagardro no. +2*avagadro no. =3*avagadro no.
I hope you understand.