A .vwx file is a 2-D or 3-D technical drawing associated with the VectorWorks CAD program. A .dwg file is another technical drawing format associated with the AutoCAD program. A .vwx file can only be converted to .dwg format using the VectorWorks program; you cannot directly import .vwx files into AutoCAD.
Open VectorWorks (not free, see Resources section).
Open the .vwx file you wish to convert
Choose "Export DXF/DWG" from the "Export" drop-down submenu under the "File" menu.
Select the .dwg file format, and choose any other options to customise the conversion, then click "OK" to complete the export.
VectorWorks is not a free program and does not have a free trial version or demo available. As such, if you do not want to buy the program to convert a few files, you may need to contact the source of the .vwx files to have the files converted for you. In addition, you may be able to find a helpful user in the VectorWorks Community or other forum to convert the files for you.