First, let's format things a little so we can see more clearly what you are sharing with us. If you put your code between <code>...</code> tags, it will keep its alignment. Here's your code again:

#!/usr/bin/perl
chdir('/home/archive/logs/old'); 
@FileNum = system("ls -t -al") ; 
chomp($month = 'date +"%b" --date "7 day ago"'); 
chomp($date = 'date +"%d" --date "7 day ago"'); 
foreach (@FileNum) { 
   if /how do I compar the date?? here { 
      system(" rm $_"); 
   } 
};
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