Examples are key, and a couple more would be helpful to make sure we really understand what you are trying to accomplish. See How do I post a question effectively? and I know what I mean. Why don't you?.

If I understand what you are saying, you want to print when you get a match on both columns, but in your original code you are only keeping track of column 2. I would use a HASHES OF HASHES structure, with

open my $FH2, '<', '/tmp/fileread' or die "unable to open file 'file' 
+for reading : $!";
open my $FH6, '>', '/tmp/tst.txt' or die "unable to open file 'file' f
+or reading : $!";

my %duplicates;
while (<$FH2>) {
    chomp;
    my ($column_1, $column_2, $column_3) = split /,/;
    print {$FH6} "$column_1\n" if $duplicates{$column_2}{$column_3}++;
}
close $FH6;
close $FH2;
open my $fh, '<', '/tmp/tst.txt' or die "unable to open file 'file' fo
+r reading : $!";
while (my $line = <$fh>) {
print $line;
}
close $fh;
[download]

where I have modified the classic code to remove duplicates from How can I remove duplicate elements from a list or array? in perlfaq4.