You need to work with lists

Choose-N from each set

my @chosen = ChooseN( 2 , \@set );
push @chosen, ChooseN( 4 , \@set );
push @chosen, ChooseN( 6 , \@set );
push @chosen, ChooseN( 8 , \@set );
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Then shuffle those playing cards :)

use List::Util 'shuffle';
@chosen = shuffle @chosen;
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And then make them presentable

my $chosen = '';
while(@chosen){
   $chosen .= join '', splice @chosen, 0, 6;
   $chosen .= ' ' if @chosen;
}
return $chosen;
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What am I doing wrong and am I even on the right track?

Not sure, but see also Opportunity to excel / Enough With The Rainbow Tables: What You Need To Know About Secure Password Schemes

And see also Crypt::RandPasswd, Crypt::PassGen, String::MkPasswd