Some filters do not work on all documents or may have some requirement that is not met. Photoshop will gray the filter out when they can not be used, Some filters don't work in 16bit color other 32 bit color, Some may not support grayscale , mapped color or lab mode. Some filters require a supported GPU and proper video drivers. If you look in your Photoshop Preference Performance section is GPU enabled and if so what advance mode is being used. I believe Liquify requires a GPU. If Enable try changing its advance mode setting. Permission errors are usually some installation problem. Some folder is being write protected for you user id.
I think my problem is installation problem. but how can I fix it?
Does your Photoshop Preference Performance section show GPU enabled? The problem may not be within Photoshop it may be with your system. You may need an updated device driver for you display adapter.
Mercury Graphics Engine
The Mercury Graphics Engine (MGE) represents features that use video card processor, or GPU, acceleration. In Photoshop CS6, this new engine delivers near-instant results when editing with key tools such as Liquify, Warp, Lighting Effects, and the Oil Paint filter. The new MGE delivers unprecedented responsiveness for a fluid feel as you work.
Did you by chance also install a CC trial (and the Creative Cloud app)?
If so, Quit and restart the Creative Cloud application: http://helpx.adobe.com/creative-cloud/kb/creative-cloud-connection-faq.html#id_10491
It should update and fix this issue. After you update the Creative Cloud app, relaunch Photoshop. Let me know if the problem goes away.
Otherwise, Make sure your user account has Read & Write access for the following path: /Users/<your user name>/Library/Preferences/AdobeOS X Mavericks: Set permissions: http://support.apple.com/kb/PH13799