This exercise is from the Core Skills section on Muting.

Here we use the thumb to mute the Low E string as we play a simple C powerchord. We'll be playing fast, using some palm muting, open stabs and dead stops. It may seem complicated, but it's not too bad because we hold the fretboard fingers on the same fret positions throughout!

The trick is to fret the C powerchord as normal - using your 1st and 3rd fingers, as shown in the ActionTab. Now bring your thumb over the top edge of the fretboard so that it lightly touches the low E string, muting it. Watch the introduction video at the start of this section again to see this type of thumb muting. It is extremely common to use the thumb to mute, so knowing how will help a lot!

One thing to bear in mind is that thumb muting will affect your fretboard hand a lot. For a start - your fretboard fingers will approach the frets from a shallow angle. This isn't good for playing lots of awkward classical guitar tunes, but it suits styles that involve lots of strumming and partial chords. This is because your fingers are naturally closer to the strings and therefore able to mute easier. In turn, this means you can strum freely without having to worry about trying to omit strings with your strumming hand, which is harder than muting.

Remember that muting is a way of controlling strings - you use it to control what ISN'T heard as much as what is heard. Practicing exercises like this will help your overall string control a great amount. Don't get frustrated - practice slowly and keep at it...with patience you will get it and your overall ability will greatly improve!