So far windows 8 really sucks! Only had this new computer 3 months. 64-bit 4.00 GB. The hard disk driver "Recovery Image (D:)" now has 681mb free of 19.3 gb! Keeps telling me "important" Check backup dish space...none available! No idea how to increase the space in (D:) although I have tried all that recommended, so far nothing works. How do you increase the backup disk space in windows 8?

You don't! You should not be doing what you are doing. That Recovery Image (D:) is not a backup disk, and you should not be writing anything to it.
This is not a backup drive. It is a recovery image provided by your computer's manufacturer (not by Microsoft). You say "So far windows 8 really sucks!" but this has nothing to do with Windows 8.
This recovery image was provided to you by your computer's manufacturer instead of an installation DVD. Its purpose is to permit you to reinstall Windows from it should that become necessary. Your computer came with instructions on how to use it.
It also came with instructions on how to burn its contents to a DVD so you would be able to reinstall Windows if your drive crashed. Following those instructions should have been the first thing you did when you got the computer. If you haven't clobbered its contents, you should do that immediately. If you no longer have those instructions, contact the manufacturer or check on their web site.

Note that this recovery image has nothing to do with Windows 8, and many computer manufacturers did exactly the same thing with previous versions of Windows.

One other point: Even if that drive were there for you to write backups to, it would be a very poor place to which to backup. It leaves you susceptible to simultaneous loss of the original and backup to many of the most common dangers: severe power glitches, nearby lightning strikes, virus attacks, even theft of the computer.

In my view, secure backup needs to be on removable media, and not kept in the computer. For really secure backup (needed, for example, if the life of your business depends on your data) you should have multiple generations of backup, and at least one of those generations should be stored off-site.

My computer isn't used for business, but my personal backup scheme uses two identical removable hard drives, I alternate between the two, and use Acronis True Image to make a complete copy of the primary drive.

I also use a pair of 16GB thumb drives for making more frequent backups of my most critical data (like financial information). For that I just drag and drop.