Latest Windows 10 update

Reimage is absolute JUNK! Stay away from it! It WILL damage your computer and is almost like malware when trying to remove it.

 Softonic is also an extremely dangerous place to download anything. It is a known site that bundles malware with its downloads. When you need to download something get it straight from the developer only.

The Windows Update was just released on Tuesday. Don't panic. Don't try to force it to download. Just leave your computer set to automatically update and it very likely will update.
The update is only an update that concerns quality improvements, no changes to the operating system. Don't be concerned. It WILL install sooner or later.

Happy to help. As I said, it is very likely you WILL get the update soon enough. Don't worry about it. There are times when simple things cause update failure, very often due to lots of traffic on their update channel. Don't worry. Keep Automatic updates turned on and before you know it the update will install.

You do need to allow your machine to automatically update. If you have been attempting to manually download and install the latest update from a couple of days ago it is likely not installing because there have been 10 updates since your last one that updated you to Build 16299.192
You can see a list of the Builds and corresponding updates here support.microsoft.com/en-us/help/4043454


Edit:three of those intervening updates are for Windows  Mobile so would  not be relevant.

Theoretically the latest update should include any you have missed but from experience this is not always the case. 

If KB4093112 has actually updated your OS will have updated to Version 1709 OS Build 16299.371. It is most likely it has installed and that pesky bug that has also afflicted some previous updates is incorrectly saying it hasn't
Type winver in the search box then click on winver run command to check.

I would download KB4093112 and do a manual install. I have done that successfully several times when Windows Update has failed in the past.

I would wait until the next Windows update is released and see if it will fix itself. A major update will arrive soon as Microsoft is about to release it's Spring Update (or whatever they are calling it) any day now. It was scheduled to be released on patch Tuesday but the pulled because it was causing BSOD's on some computers.

Personally, I think this is rather drastic. I would go ahead and use it.
Earlier you said this:

Is that your anti-virus program?

The thing is you are trying to install an update that requires OTHER updates first. You need to install those before you can get the one you are waiting to receive. As Everton said earlier, your latest update was released in January, you don't have any other the others released.
Try installing those manually.

Go to the link she gave you and start with the one AFTER the one you already have. There is a link to the catalogue with each page so you can download and install them manually. Read each one because as she said some of these are for mobile devices and would NOT apply to your laptop.

Are you absolutely certain that you tried to install the correct version of KB4074588? There are four copies offered but only ONE of those will be for your computer.
There is one for x64 based system, one for Windows Server x64 based, one for x86 based system and one for ARM64 based systems.

For the KB4093112 there are 8 different copies but only ONE of those would be for your computer.

Did you get this one to install manually?

KB4058258

When you do these manually they should be done one at a time. Download, install, reboot and then on to the next one. Rebooting to finish install is standard recommendation. Many times the automatic updates will also do this automatically. This allows the update to install the second the computer is booted before anything else has started up, that way there can be no interference from some other process.

You might also try running the Windows Update Troubleshooter. Very often this will fix any problems. Clicking the link will give you the executable application. Save it on your computer, close all other applications and run the Troubleshooter.

joel, I tried it but it did not make any difference.

Sorry, it worked for me once but I knew it was a long shot.
The previous advice about waiting for the next update seems right on.  Many people have your same issue.

See:
answers.microsoft.com/en-us/windows/forum/windows_10-update/last-failed-install-attempt-on-06-jan-18/717f2216-ef4d-4c67-8926-5b3c2c9867f7

Joel

I went to this site but got stumped when I could not remember my administrator password at the command prompt since I never use it. I am the only one that uses this laptop. Usually I write my passwords in a book but I cannot find it. Grrrrrrr
I guess I am stuck for now

Judy, I went through the steps on the site that Everton gave me. The first ones were OK but then I needed my admin password at the command prompt. You gave me the site for Windows Troubleshooter, it never asked for my password. Those two sites are different. The Troubleshooter site did not fix my problem.

This is the page I get when I use Everton's URL

I ran the Troubleshooter again just now. This was the third time and it said "fixed" but after checking, it still said my computer is at risk. When I click "No" at the this step on Everton's site it carries on for several steps with me choosing "No" I get to the command prompt which asks me for me Administrator password which is where I am stumped.
I guess at this time I have to give up and wait to see what happens with the next Windows Update. If that does not fix it, off it goes to the computer store.