If I'm not mistaken, your are trying to print out lines in which the "symbol" starts with the string "Hox". If that is the case, I see no need for building up a hash at all; just process the lines as you read them in. If you really want to re-order the columns, then this might be a simpler way to do things (UNTESTED):

use strict;
use warnings;

open INPUT,"<MOUSE_TF1.txt" or die "can not open MOUSE_TF1.txt: $!";
open OUTPUT,">HOX_GENE_TF.txt" or die "can not open HOX_GENE_TF.txt: $
+!";   
print OUTPUT "MOUSE TRANSCRIPTION FACTORS IN THE HOX GENE FAMILY\n\n\n
+";
print OUTPUT "ENSEMBL GENE ID \tSYMBOL \tCHR\tSTART\t\tEND\t\tSTRAND\n
+";
while (<INPUT>){
  chomp;
  my ($id, $cname, $start, $end, $strand, $sym) = split /\t/;
  # select Gene Symbols belonging to "Hox" family and print
  if ($Sym =~ /^Hox/) { print join("\t", $id, $sym, $cname, $start, $e
+nd, $strand), "\n" }
}
close INPUT;
close OUTPUT;
[download]

If you are willing to preserve the column order from the input, this simplifies even further to:

use strict;
use warnings;

open INPUT,"<MOUSE_TF1.txt" or die "can not open MOUSE_TF1.txt: $!";
open OUTPUT,">HOX_GENE_TF.txt" or die "can not open HOX_GENE_TF.txt: $
+!";   
print OUTPUT "MOUSE TRANSCRIPTION FACTORS IN THE HOX GENE FAMILY\n\n\n
+";
print OUTPUT "ENSEMBL GENE ID \tCHR\tSTART\t\tEND\t\tSTRAND\tSYMBOL\n"
+;
while (<INPUT>){
  chomp;
  my @items = split /\t/;
  # select Gene Symbols belonging to "Hox" family and print
  if ($items[5] =~ /^Hox/) { print "$_\n" }
}
close INPUT;
close OUTPUT;
[download]