I'm following a tab and I encountered what is pictured below. How do I prevent the 4th string from ringing when I play this?
You could use the pick to sound the fifth string, and the fingers to pluck the top three strings. Some people call this hybrid picking. You might pick the fifth string and drag the nail of your middle finger across the top three strings at the same time.
Another alternative would be to get one of your fretting-hand fingers (probably your second finger if you fret the note with the first) in there to mute the fourth string. Then you can drag the pick across all of the strings.
I find myself using all of these techniques (but the first and the last the most often), and the larger context of what I am playing determines what happens when I play.
As tabbed this looks like a
Am7 chord with the 4th string omitted. If you play
E on the 4th string, 2nd fret it will make an octave with the open
E string then you can play all 5 strings.
Of course that isn't what the tab says to play, so if you want to be faithful to the tab, you have to use one of @DavidBowling's excellent suggestions.
It depends on the music and the nature of the tab (is it someone's arrangement of a song?) to decide if adding a note is OK or not.