since few weeks ago I can not open downloaded docx files. What is the reason? thanks for any helpful answer.

What happens when you try?  Is there any error message?

This is my (expanding) list of things to try when Office 2013\365 won’t start or crashes:

See the KnowledgeBase article “Office 2013 applications crash on launch at the splash screen” at:

http://support.microsoft.com/kb/2813143

Or see the KnowledgeBase article Error: “Something went wrong and we can't sign you in right now” when trying to install Office 2013 at:

http://support.microsoft.com/kb/2811180/en-us/

Also see my response in

http://answers.microsoft.com/en-us/office/forum/office_2013_release-word/microsoft-word-2013-has-stopped-working/67b81016-849f-481a-bce5-bf04797ac03b

Do you have Abbyy Finereader installed on the PC? A number of people have reported that removing it overcomes problems with 2013

Do you have “Fun Tools” add-in? A number of people have reported that removing it overcomes problems with 2013

Do you have Toshiba Book Reader installed on the PC?  It has been reported that uninstalling that brings Office back to working status.

Do you have the Acrobat PDFMaker add-in.  It has been reported that uninstalling that overcomes an issue with a message appearing that states "The document contains macros. Macro support for this application is disabled. Features requiring VBA are not available. Would you like to open this document as a read only?"

Also see: http://answers.microsoft.com/en-us/office/forum/office_2013_release-word/microsoft-word-has-stopped-working-when-i-close/8375b5b6-4f7e-46ed-a02b-90152ecad287#LastReply and

http://answers.microsoft.com/en-us/office/forum/office_home-word/word-and-excel-2013-crashing-on-windows-7/5389390c-e989-4c8e-8fe0-62673f1410ce?page=4#LastReply

It appears that there may be some hardware incompatibilities as well. 

From the File tab, select Options and then click on Advanced and then in the Display section of the dialog, check the box for Disable hardware graphics acceleration

For the error message "There was a problem sending the command to the program", use Windows Explorer to access the C:\Program Files\Microsoft Office\Office15 folder and right click on WINWORD.EXE then on Properties, go to the Compatibility tab and uncheck all the boxes.