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Updated: $HoH{$group} is a reference to a hash. I refactored your code as follows:

#!/usr/bin/env perl

use warnings;
use strict;

my %HoH = (
    flintstones => {
                        lead => "fred",
                        pal => "barney",
    },
    jetsons => {
                        lead => "george",
                        wife => "jane",
                        kid => "jane",
    },
    simpsons => {
                        lead => "homer",
                        wife => "marge",
                        kid => "bart",
    },
);

my $total_jane_count = 0;
for my $group ("simpsons" ,"jetsons" ) {    
    my %family_hash = %{ $HoH{$group} };
    for my $name (values %family_hash) {
        if ($name eq 'jane') { $total_jane_count++ }
    }
} 
print "total_jane_count = $total_jane_count\n";
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This prints:

total_jane_count = 2
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