How to damping strings on acoustic guitar

I am not sure how to do the heavy damping as shown in the tab below. I am learning on an acoustic guitar, just putting light pressure on the strings kills the sound and makes a odd noise. How do I do the dampening they indicate?

e|--2-------x---------------|-----------------5-------|
B|--1-------x-------3-----3-|-5-------3---------------|
G|--2-------x---------------|-------------------------|
D|--0-------x---------------|-------------------------|
A|--0-------x---------------|-------------------------|
E|--------------------------|-------------------------|

x - play 'note' with heavy damping

You most damp the strings with your right hand!
It is not easy to explain but it is a rock position.
You mute the strings with your underside of your palm at the same time you hit the strings.
Keep Rocking

It's actually called "Palm Muting" and it's usually indicated in tabs with a "pm" under the tab lines. Just as the other guy said though, you mute the strings with th side of your right hand. This gives the strings a more "THUD" or "CHUG" like sound... It's definitely an easy technique that is very widely used. just practice it and do it till it sounds right to you. Rock on \m/

Also work on muting with your fretting hand, with time you'll learn the subtleties between these two muting methods. Good luck!

I think your already doing it, but it is much more prominent on a clean electric guitar.
A good example is: Dire Straits - Brothers in Arms -Track 1 - so far away

Ok, I just wanted sure if I understood the muting concept...now back to practice.