This exercise is from the Core Skills section on developing Speed Techniques. As usual, check out the normal speed audio first.
The following series of legato exercises are very useful. Legato is a different way to play fast sequences of notes, without using alternate picking. So, Legato specifically means using hammers, pull offs and slides instead. These techniques all create notes using the fretboard hand rather than the picking hand. Many guitarists opt to use legato techniques instead of picking to afford speed. We recommend learning both methods.
Here we use hammers in 3's along each string. Notice that each string is initially picked (you can't avoid picking altogether when using legato techniques). But notice that each pick is a downstroke. Now, when you get really fast at this exercise you should notice that you are actually doing more of a controlled strum across the strings, with the hammers falling between as you pick down across the strings. In a way this is like sweep picking, and applying hammers.
Do it as we show here, using the downstrokes per string. Don't be tempted to alternate pick each string. Because when it gets to full speed, the downstrokes will actually work out to be faster!
Also, remember that with fast hammers it is important to remove a finger as soon as the next note is being played. We discussed this principle in our First Exercise. It also applies here. All your fretboard fingers should be constantly moving through this exercise.
Like our previous exercises, focus on getting the timing right. It is important that each note lasts the same amount of time.