x86 is the 32-bit version (x64 is the 64-bit version)
Every browser needs the code (add-ons) to process the web items it finds (that aren't supported natively by the browser). Apparently your Firefox and your IE 64 have the add-ons they need to make it work; your IE 32-bit does not. If your PDF handler is from Adobe then visit the Adobe site.
What I would like to see is the error you get in IE 32-bit, as well as a screenshot of this drop down menu you get in IE 64.
You can upload your screenshot to your next post. Simple take the screenshot and store it on your hard drive then come here and start a post, see ...