There is no built-in way to do this in Word, and I think you will find it
more trouble than it's worth (not to mention that a 20-page booklet would be
impossible with this imposition--it would have to be 16 or 24).

AutumnFire1 spake thus:

First of all; yes, you're using the wrong program. Word is extremely
weak in this area. This job would be much more easily and rapidly done
with a *real* page-layout program, like Adobe InDesign. (Forget
Publisher--it's a piece of sh.t.)

Having said that, you may be like me, in that you're not particularly
eager to shell out $$$ for new software.

Someone wrote a clever macro that lets Word print booklets:
http://word.mvps.org/FAQs/Formatting/BookletPrinting.htm.

Warning: you need to know at least enough about VBA ("Word Basic") and
macros to get yourself into trouble, and probably a little more to get
yourself out of trouble.

The macro does work. Any problems you encounter are going to be just
with setting up the document to print correctly (correct location on the
sheets, etc.). And a 20-page booklet is no problem: first of all,
booklets like the one you want to print come in multiples of 4 pages,
and besides, the macro will pad your document to the nearest 4-page
boundary with blank pages anyhow. Give it a whirl.