You're compiling the same regular expressions over and over again, once for every line in the second file. Note the use of qr// below.

#!/usr/bin/perl -w

use strict;

my @regexps;

{
   my $fn = $ARGV[0];
   open(my $fh, '<', $fn)
      or die "Cannot open pattern file \"$fn\": $!\n";

   while( <$fh> ) {
      chomp; 
      my ($pat) = /(\S+)\s+\S+/
         or next;
      push @regexps, qr/$pat/;
   }
}

{
   my $fn = $ARGV[1];
   open(my $fh, '<', $fn)
      or die "Cannot open data file \"$fn\": $!\n";

   while ( <$fh> ) {
      chomp;
      my $cnt = 0;
      for my $re (@regexps) {
         ++$cnt if /$re/;
      }
      print "$cnt $_\n";
   }
}
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Other improvements:

• Added "use strict;", a tool that will help you find many errors.
• Since you weren't using the values of the %href, I got rid of it.
• Switched map for for since you discard the return value returned by map.
• Changed global variables FH and FD into lexicals.
• Used safer 3-arg open.