Clearly, in one formula unit of #Co(ClO_4)_2#, there are #8# oxygen atoms. Agreed? In one formula unit of #Co(ClO_4)_2*6H_2O#, there are #14# oxygen atoms. Equivalently there are 14 oxygen atoms per formula unit of the solvate.
And in a #1*mol# quantity of #Co(ClO_4)_2*6H_2O# there are thus clearly #14xx1*mol# oxygen atoms. I use the mole as a number, just as I would use a #"dozen"# or a #"score"# or a #"100"#, and of course the #"mole"# IS a number, i.e. #N_A=6.022xx10^23*mol^-1#.
And thus number of oxygen atoms in a #"mole"# of #Co(ClO_4)_2*6H_2O#,
#=14*molxxN_A=14*cancel(mol)xx6.022xx10^23*cancel(mol^-1)#
#~=9xx10^24" oxygen atoms, a number as required. "#
And in #3.42*mol#, there are #~=3.1xx10^25" oxygen atoms."#
