Both the Microsoft Office 2004 for Mac 11.5.0 Update Package and the Open XML File Format Converter for Mac are available for free. Another way that you can resolve the .docx dilemma is to use Zamzar's online file converter (see screenshot below) to downgrade the .docx file to the .doc format. Choose the .docx file, select the file format (.doc) that you wish to convert the file to, enter your email address so that Zamzar can send the converted file to you, and then click the Convert button. You'll receive the converted file shortly.
This tip comes to you via Jenny Kortina over at The Apple Blog.