We apologize for the inconvenience caused, as per the description above, Acrobat Pro X is not starting, is that correct?
I have checked the record with your current Adobe ID and found that you have a registered license of Adobe Design Standard CS 6 and Acrobat Pro X is a part of this suite.
Try to launch the Acrobat Pro X by right-clicking on it and choose Run as Administrator and see if this brings the Acrobat Pro X.
Try resetting the preferences of Acrobat, to reset the preferences, refer to How to reset Acrobat Preference settings to default.
If the issue persists, please uninstall Acrobat Pro X from the machine, reboot the machine, and download the setup of Design Standard CS 6 from Download Adobe Creative Suite 6 applications
Run the setup and choose Custom installation and install Acrobat Pro X, and complete the installation process.
Note: Acrobat 10 and CS 6 is already declared as an end of support products, and above mentioned suggestions/steps may or may not work. End of Support means that Adobe no longer provides technical support or distributes runtimes. This policy affects product and security updates for all derivatives of a product or product version (localized versions, minor upgrades, operating systems, dot and double-dot releases, and connector products). For detailed information, please refer to End of support for Acrobat X and Reader X and Adobe Support Policies: Supported Product Versions
Feel free to update this discussion for any further assistance.