The DOCX format is the new Microsoft Word format that is readable by Office 2008 for Mac or Office 2007 for Windows.
So if you already have a copy of Office 2004 for Mac you will need a special plugin to allow you to open the document in your existing copy of Office which iis included in the Microsoft Office 2004 for Mac 11.5.0 Update Package http://www.microsoft.com/downloads/details.aspx?FamilyId=B6D69814-0995-490D-909A-5EC6AE6F64F0&displaylang=en
If you do not have Office 2004 or 2008 then your only option would be to use a converter like the free online DOCX converter here http://www.docx-converter.com/ and then use it to convert the DOCX file to a TXT file which your Mac can then open and use.
Take a look and let me know if you need more info or clarification
Can you tell me what version of office you have and what program you are using to handle your zip files?
Can you download and install the free version of Stuffit expander from here http://download.cnet.com/StuffIt-Expander-2010/3000-2250_4-10653042.html
Once it is downloaded can you then restart your Mac and then see if you can now double click the ZIP file and see the contents of the compressed file
Can you follow the instructions from this XXXXX XXXXX article and use it to select the ZIP file then associate it with stuffit http://www.askdavetaylor.com/how_do_i_associate_a_file_with_an_application.html
Once you are done let me know if the file will now open
How are you getting the DOCX files?
Is it by email, and if so are you saving the attachment to your machine before you try and open it?
When you save them to the desktop can you change their default program?
When you get the attachment in your email can you save it (Drag and drop the attachment) to yur desktop and once it is on your desktop can you then use the instructions in the link I gave you earlier to set the file association with stuffit and then let me know if you can open the file from your desktop.
In that case cna you try dragging the ZIP file from your desktop over the stuffit icon and tell me what happens