Another solution, this one relying on base conversion (base 10 to base 6):

my @letters = qw( A B C D E F );

for (0..6**4-1) {
   use integer;
   my $num = join '', map $letters[$_], $_/6/6/6 % 6,
                                        $_/6/6   % 6,
                                        $_/6     % 6,
                                        $_       % 6;
   print("$num\n");
}
[download]

If @letters and $len are variable, try this generalization:

my @letters = qw( A B C D E F );
my $len = 4;

sub convert {
   my ($num) = @_;

   use integer;

   my $base = @letters;
   my $rv = '';

   for (1..$len) {
      $rv = $letters[$num % $base] . $rv;
      $num /= $base;
   }

   return $rv;
}


print(convert($_), "\n")
   for 0..@letters**$len-1;
[download]