Keeping in mind all of Corion's expert advice, here's a working version of your code, assuming counttext.txt exists and is accessible:

#!/usr/local/bin/perl -w
use strict
print "Content-type: text/html\n\n";
my $counttext = 'd:/xxx.xxx.xxx.xxx/perl/thecounter/counttext.txt';
my $thenumber;
open(COUNTTHIS, "< $counttext") or die "I can't open counttext: $!\n";
$thenumber = <COUNTTHIS>;
close(COUNTTHIS);
print "$thenumber<br>";
++$thenumber;
print "$thenumber";
open(OUT, "> $counttext") or die "I can't open counttext: $!\n";
print OUT $thenumber;
close(OUT);
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