my $dir = "/my_dir";
opendir DIR, $dir or die "$dir: $!\n";

my %subdir;
while ( my $month_dir = readdir( DIR ) {
    next unless ( $month_dir =~ /^\d{8}$/ );
    $subdir{$month_dir} = -M $month_dir;
}

my $latest_dir = ( sort {$subdir{$a}<=>$subdir{$b}} keys %subdir )[0];

# ...

##</code><code>##

my $latest_dir =
  ( map{s/(....)(....)/$2$1/; $_} sort map{s/(....)(....)/$2$1/; $_}
    grep /^\d{8}$/, readdir DIR )[-1];