Head the other responders' replies. Failure to de-reference your hash and array are the source of the difficulty as the other responders noted.

Here is a quick, short set of code that does what I believe your looking to do. I include it just so that you can see one way to do it. Of course, as in all of Perl, TMTODI.

Cheers.

#!/usr/bin/perl
use strict;
use warnings;
my $VAR1 = {
          'A2M' => [
                     'C972Y',
                     'A423W'
                   ],
          'A4GALT' => [
                        'W261X',
                        'P251L',
                        'P251S',
                        'A219V'
                     ]
        };

my $numKeys = scalar(keys %{$VAR1});
print "gene total x\n";
foreach my $key (keys %{$VAR1}){
  my @values = @{$VAR1->{$key}};
  my $numValues = scalar(@values);
  my $numXs = 0;
  $numXs += ($_ =~ /X/g)?1:0 foreach(@values);
  print "$key $numValues $numXs\n";
}
exit(0);
[download]

The resulting output is:

gene total x
A2M 2 0
A4GALT 4 1
[download]

Which is what I believe you are after.

The only difficulty is that the pattern match, $_ =~ /X/g is not very general...it wouldn't, for instance, see multiple occurances of 'X' in a value (you, the OP, didn't specify what to do if such an occurance presented itself) nor would it distinguish upper case 'X' from a lower case 'x' (you didn't specify if that mattered). But I figured either you'd already know how to handle those situations or they would be good explorations of Perl for you.

Also note that I just initialize the hash with the example that you gave rather than reading it in from a file because I felt that it would just obscure the main body.