use strict and warnings and use lots of print's and file checks (-e):

my @bookNameArray;
my $bookName;
my @bookFileName;
for(my $h = 0; $h < scalar(@bookFiles); $h++){  
   @bookNameArray = split(/_/ , $bookFiles[$h]);
   @bookFileName = split("/" , $bookFiles[$h]);
   $bookName = $bookNameArray[-2];
   my $newdir = $dir . "/Book Chapter/" . $bookName;
   print "newdir >>>$newdir<<<\n";
   mkdir($newdir) or die "cant mkdir $newdir: $!"; 
   my $src = $bookFiles[$h];
   print "src>>>$src<<<\n";
   my $dst = $dir . "/Book Chapter/" . $bookName . "/" . $bookFileName
+[-1]);
   print "dst>>>$dst<<<\n";
   if (-e $src) {
      print "$src exists\n";
   } else {
      print "$src does not exist\n";
   }
   # same -e check for dst
   move($src, $dst) or die "cant move : $!";
}
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See also Basic debugging checklist