See possible fixes here.
Some have reported success simply by reinstalling the update.
Or download and apply, or reapply, the 10.6.8 Combo update first, then apply the Security Update again.
I'd suggest starting with the simplest of these fixes, so look them over first.
Thanks for such a helpful reply when I was losing hope!
I browsed the links you sent, and it helped me muster the courage to do a variation on the advice from Apple since following their instructions in the article to a T did not solve the problem.
In case it helps others:
Instead of moving Mail 4.6 to Applications folder (it was already there) like Apple advises
I put Mail 4.6 in the trash, and moved Mail 4.5 to Applications (it was on Desktop)
then followed the instructions in the Apple article linked above
Mac Os X 10.6.8 Update Combo v. 1.1
Security Update 2012-004 (snow leopard)
It works! I now have Mail 4.6 working on my computer.