use strict; use warnings;
my $input = '1234562234563334564444565555566789';
my @sets_of_six;
while (length $input > 6){
   my $front = substr($input, 0, 6);
   $input    = substr($input, 6);
   push @sets_of_six, $front;
}

push @sets_of_six, $input if length $input > 0;
use Data::Dumper;
print Dumper( @sets_of_six );
[download]

while (length $input > 6){
   my $front = substr($input, 0, 6);
   $input    = substr($input, 6);
   push @sets_of_six, $front;
}
[download]

This can be done slightly more compactly by having the initial substr remove the leading characters as it retrieves them:

while (length $input > 6){
   my $front = substr($input, 0, 6, '');
   push @sets_of_six, $front;
}
[download]

(Or even get rid of $front entirely with

while (length $input > 6){
   push @sets_of_six, substr($input, 0, 6, '');
}
[download]

if you don't think that's becoming too unreadable.)

I think you show the progression from extremely simple to comprehend but overly verbose, gradually into a much more acceptable solution in a very fine way that should be easy to follow and learn from.
I think that your progression ends at a nice place too, unless one work in a shop where perl is a primary language.
My preference is unpack, as BrowserUk demonstrates,
cheers