If the page returns with a server error (5xx) you should check the web server log to see what happened.

In this case, my best guess is that the server has not permissions to open graph.png for output; in general it is a bad idea using a relative path in a cgi script, for you really don't know which the current dir is at execution time. Try again, specifying an absolute patch name in your open, and a path in which the user running the web server has permission to write into.

... my best guess is that the server has not permissions to open graph.png for output ...

It's also a good idea to let yourself know about such problems as they develop. Something along these lines might be informative:

my $filename = 'graph.png';
open my $fh, '>', $filename or die "opening $filename: $!";
binmode $fh;
print $fh $mygraph->plot(\@data)->png or die "writing $filename: $!";
close $fh or die "closing $filename: $!";
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Indeed ... even better would be to use CGI::Carp; to allow the errors &/or warnings to be seen by/in the browser, otherwise they'll only ever be seen in the server logs - but this may be a/the requirement.
A user level that continues to overstate my experience :-))

Where is your shebang? Where is your CGI object? Where are your strictures?

#!C:\perl\bin\perl.exe -wT

#always
use strict;
use CGI ':standard';
#tell CGI to print fatal errors to the browser
use CGI::Carp qw(fatalsToBrowser);
use GD::Graph::bars;

#you need to actually create a cgi object, not just include the module
my $q = new CGI;

# Both the arrays should same number of entries.
my @data = (["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug",
             "Sep", "Oct", "Nov", "Dec"],
            [23, 5, 2, 20, 11, 33, 7, 31, 77, 18, 65, 52]);


my $mygraph = GD::Graph::bars->new(500, 300);
$mygraph->set(
    x_label     => 'Time taken (Hrs) for compilation',
    y_label     => 'Environments',
    title       => 'Production taken in the Week of $file',
) or warn $mygraph->error;

open FH, "> graph.png";
binmode FH;
print FH $mygraph->plot(\@data)->png;
close FH;

#this is all wrong
#You're mixing your methods of printing the image.  If you're going to
#print it directly, there's no need to save it to file.  But then you
#can't be printing text to the screen first.  If you're going to print
+ it
#inside an image tag and referencing a file, you can't just dump the p
+ng data
#to the screen.
#-- you need to look at the cgi doc again


#print "Content-type: image/png\n\n";
#print "raja\n";
#print $myimage->png;


PRINT_FROM_FILE();
#----OR----
#PRINT_IMAGE_DIRECTLY($mygraph);

sub PRINT_FROM_FILE{

#print a simple page referencing the file you created earlier
  print header
        , start_html
        , img ({src=>"/graph.png"})
        , end_html;
}
      
sub PRINT_IMAGE_DIRECTLY {
  my $mygraph = pop(@_);
#  my $myimage = $mygraph->plot(\@data) or die $mygraph->error;

  print header('image/png')
        , $mygraph->plot(\@data)->png;
}
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I'm wonder why you use this line:

print "raja\n";
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