Display post from one category in another category

I am trying to create a huge site and I need to display post from one category in another. Example: the latest post from categories 2,3,and 4 should display in category 1. Is this possible?
<?php $recent = new WP_Query("cat=12&showposts=3"); while($recent->have_posts()) : $recent->the_post();?>
This is as far as I got with my limited php skills, but it is only displaying post from it self. Like it was designed to do.
Any help would be appreciated. Thank you in advance.