So measure 1 of this 4 measure section is just 8 eighth notes on your low open E.

They should be palm muted.  Which would be written with a pm.......... above the notes.  I forgot to add that above the staff.

The reason for leaving one measure rest before repeating is to ingrain 8 eighth notes in 1 measure.  This can not be stressed enough, from an educational view we want to know exactly what 8 eighth notes feels like making up 1 measure in 4/4.

The guys in Metallica down pick this riff although as you speed it up you may need to play it using alternate picking.  Ideally we would get equally good at both at all speeds 🙂

But please note that most people tend to find one way gets faster much more quickly then the other.

In the 2nd measure of this 4 bar riff we get to play some power chords.  Because of the slides, you will not pick any of the A power chords (A5).  You will down pick the power chord before and then slide to the A5.

Practice it where you always have control.  If you are playing it at a tempo and it is sloppy, slow it down until you have control.  Each day try to increase the tempo just a bit but remember if it gets sloppy, slow it back down.  Probably one of the most important lessons that I ever learned playing guitar (or any instrument for that matter).