There are three issues here potentially.
1. Is your expression and HTML correct?
Your div doesn't have a border width (from what you've posted) so you might not get a border. Try:
<div class="foo bar"></div>
with
div.foo.bar { border: 1px solid black; }
2. Does you div have any height?
Your div (based on what you've posted) has no height. Now on some browsers that'll render as a solid line of the border thickness. Depending on neighbouring elements and border collapse settings (particularly on Firefox more than IE/Safari though), that border may disappear in some circumstances.
3. IE6 doesn't support multiple class selectors correctly
Multiple class selector does not work (correctly) in IE6. See multiple classes and the browser support table.
Usually the trick here is to nest the divs:
<div class="foo"><div class="bar"></div></div>
and then of course:
div.foo div.bar { ... }
Not the same thing obviously but you don't have much choice. The other alternative is to combine the classes manually:
div.foo { background: red; }
div.bar { border: 1px solid black; }
div.foobar { background: red; border: 1px solid black; }
<div class="foobar"></div>
Again, far from ideal. But there's only so much you can do on IE6.