$count{$_}++ for $string =~ /../g;
[download]

Update: With the clarifications of the problem statement:

while( @strings ) {
    my( $x, $y )= splice @strings, 0, 2;
    my %count;
    while(  $x =~ /(.)/g  ) {
        my $x1= $1;
        $y =~ /(.)/g
            or  die "...";
        $count{ $x1.$1 }++;
        # Or replace all of the above with:
        #$count{ "$1" . ( $y =~ /(.)/g ? "$1" : '' ) }++;
    }
    print join " ", %count, $/;
}
[download]

with the (simple) cleaning up of the output left as an excercise.