Your description is ambiguous. With the second string all the same char we have to infer either you want

1. char1 str1 against char1 str2, char2 str1 against char2 str2 or you want all the permutaions ie
2. char1 str1 against char(1..n) str2, char2 str1 against char(1..n) str2....

I am assuming you want all the permutations. There are two general approaches. Brute force and the more clever approach. Brute force won't scale well as it is O(n^2). The clever approach is 0(n) plus an O(n^2) whisker that represents the number of possible tokens. As you can see both approaches yield the same results. Assuming those are the results you wanted ;-)

use Data::Dumper;

my $site1 = 'AATKKM' x 20;
my $site2 = 'GGGGGA' x 20;

# brute force
my (%hash, $loops);
for my $base1( split //, $site1 ) {
    for my $base2( split //, $site2 ) {
        $hash{"${base1}_$base2"}++;
        $loops++;
    }
}

# precount incidence of tokens
my (%s1, %s2, %hash_e, $loops_e);
do{ $s1{$_}++; $loops_e++ } for split //, $site1;
do{ $s2{$_}++; $loops_e++ } for split //, $site2;

# still loop within loop but the are now far fewer loops to do
# as we only do one per token pair and calculate the total pairs
# from our precount data
for my $base1( keys %s1 ) {
    for my $base2( keys %s2 ) {
        $hash_e{"${base1}_$base2"} = $s1{$base1}*$s2{$base2};
        $loops_e++;
    }
}
print "Brute force loops $loops\nEfficeient Loops  $loops_e\n\n";
print Data::Dumper->Dump([\%hash, \%s1, \%s2, \%hash_e], [qw( hash s1 
+s2 hash_e)] );

__DATA__
Brute force loops 14400
Efficeient Loops  248

$hash = {
          'T_G' => '2000',
          'A_A' => '800',
          'T_A' => '400',
          'M_G' => '2000',
          'M_A' => '400',
          'K_G' => '4000',
          'K_A' => '800',
          'A_G' => '4000'
        };
$s1 = {
        'A' => '40',
        'K' => '40',
        'T' => '20',
        'M' => '20'
      };
$s2 = {
        'G' => '100',
        'A' => '20'
      };
$hash_e = {
            'T_G' => '2000',
            'A_A' => '800',
            'T_A' => '400',
            'M_G' => '2000',
            'M_A' => '400',
            'K_G' => '4000',
            'K_A' => '800',
            'A_G' => '4000'
          };
[download]