my @dirs = `ls /var/log/HOSTS/*/*/$year/$month/$day/*`

I'm not sure where you want to go with this, but I assume you want to do something in each directory that exists for the day/month/year for each logged host.

The canonical Perl way of doing this (without relying on an external program) is to use the venerable File::Find module.

use File::Find;

find(
  sub {
    return unless
      $File::Find::name =~ m{^/var/log/HOSTS/([^/]+)/([^/]+)/(\d+)/(\d
++)/(\d+)/(.*)$};

    my( $dir1, $dir2, $year, $month, $day, $file ) =
      ( $1,    $2,    $3,    $4,     $5,   $6    );

    # do stuff with $file
  },
  '/var/log/HOSTS'
);
[download]

Or if you do just want to get the names of the directories that actually exist, you would write something like:

  $File::Find::name
    =~ m{^/var/log/HOSTS/([^/]+)/([^/]+)/(\d+)/(\d+)/(\d+)$}
      and push, @dirs, $File::Find::name;
[download]

print@_{sort keys %_},$/if%_=split//,'= & *a?b:e\f/h^h!j+n,o@o;r$s-t%t#u'