I am trying to delete my existing windows partition using disk management, when I am right clicked on the selected partition the 'Delete Volume' and 'Extend Volume' options are grayed out ( doesn't allow deletion and extension), and I can not also change or remove the drive letter of the disk which has above problem. And Another partition that I don't want to change anything it allows all the options. Why does this happen?
The Delete Volume and Change Drive Letter and Paths... options for your drive D: are not available because there is a Page File on it. If you take a close look at your first picture, you can see that the text under IT World (D:) reads Healthy (Page File). Before you can delete that volume or change its letter, you will have to tell Windows not to put a page file on it - if you need help with that, see the top answer in this question and set No paging file for drive D:. Once you've done that, reboot. The options to delete and change letters should now be available.
The Extend Volume option is not available because partitions on Basic disks can only be extended if there is free (unallocated) space remaining on the same drive and that free space is directly adjacent to the partition you wish to extend. In your current setup, there is no free space left, but if you delete volume D:, you will be able to extend drive H: (and only H:). If you wish to extend a drive different from H:, you will need to delete a different partition or consider converting your disk to a Dynamic disk. To do that, check out the official guide, but make sure you understand the dangers and implications of Dynamic disks first.