With Egyptian hookahs, they are designed in the traditional manner. This means that the whole stem is all one piece, including the down stem. The best way to clean it is plug one end of the stem, pour in your cleaning agents, then plug the other end and shake it around. The middle (core) of the stem is usually one long tube straight down the middle so it's very easy to clean. You can also use a stem brush, available in a ton of places online, and you insert it into the stem and scrub it clean.
You cannot dismantle the stem or hose ports in a Traditional stem, only in Mod stems (JandR Syrians, Mya hookahs, Mod Hookahs on Hookah-shisha.com).
To clean out the tubes inside the heart (that lead to the hose ports and the purge valve) you can use pipe cleaners or a stem rod. They are a bit harder to clean, but you can find your own way.