Hi Madugu702
I'm not sure if you're still having trouble updating to Mojave, and if that's your question.
I followed Eau Rouge's advice (17th January), as follows, and it worked beautifully. However, I neglected the final step of copying the install Mojave from Applications onto a USB stick...that would be handy.
So I'd recommend you do that.
Also, check that you have latest version (which Eau Rouge points out) and update if necessary. I didn't, so followed that step before downloading and installing Mojave. So here are the steps I followed.
Good luck....
In your first post under the screenshot you have posted your version of High Sierra as being 10.13.1, I think you may have better success if you updated High Sierra to its last version 10.13.6 before attempting to install Mojave.
Download this, Download macOS High Sierra 10.13.6 Combo Update once downloaded double-click to install.
It is also important to remember if you are going to be downloading large files like installers or updaters to have your Mac connected to your router by cable rather than wifi, this will ensure you have a faster more robust connection. Once you have downloaded Mojave, and before you start the installation process look in your Applications folder for Install mcOS Mojave.app.
Copy this over to an external drive or USB stick and keep it safe, the one in the Applications folder self deletes once Mojave is installed. Having the copy is handy incase you need to reinstall or want to install it on another Mac and don't want to go through the tedium of having to download again.
But the way, I also restarted in Safe Mode at one point, and that made all the difference. See https://support.apple.com/en-au/HT201262