This will work on the current folder:

#!/usr/bin/perl

use warnings;
use strict;
use File::Copy;

while (my $filename=<*.txt>) {
    next if !($filename =~ m/_(\d{6})\.txt\z/);
    my $date=$1;
    if (!-e $date) {
        mkdir $date;
    } else {
        if (!-d $date) {
            die "$date already exists and is not a folder";
        } elsif (!-x $date) {
            die "Wrong permissions on preexisting folder $date";
        }
    }

    move($filename,"$date/") 
        or die "Couldn't move $filename to $date: $!";
}
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If you want to remove the _yymmdd from the file name while moving, replace the last line with

my $newname = $filename;
$newname =~ s/_\d{6}//;
move($filename,"$date/$newname") 
    or die "Couldn't move $filename to $date/$newname: $!";
[download]