This code build a new hash with the values as keys and collect all keys that point to this value.

my %h = (
          a => 10,
          b => 10,
          c => 'd',
          e => 'd',
          f => 'a',
);

my %x;
while ( my ( $k, $v ) = each %h ) {
  push @{ $x{$v} }, $k;
}

__END__
$x = {

          'a' => [
                   'f'
                 ],
          '10' => [
                    'a',
                    'b'
                  ],
          'd' => [
                   'e',
                   'c'
                 ]
};
[download]

If you just want to remove the duplicates try:

my %n = reverse %h;
%n = reverse %n;
[download]