When I looked at the diagram, I guessed the root was probably the F on the 3rd fret of the 4th string. The next note is one string higher and 2 frets lower, making it a minor 3rd. The note on the 2nd string is one fret higher than the root on the 4th string. If this was on any other string, it would be a major 7th. But because it's on the 2nd string (which is tuned a 3rd above the 3rd string instead of a 4th the way the others are) it's the flat 7th. The last note is a one string higher and one fret lower, making it a major 3rd above the 7th. This makes it the 9th. You can also just see that the note is the G above the octave, making it the 9th.

We end up with F, A flat, E flat and G. As @Jason Smith pointed out, this is an F minor 9th chord with the 5th (the C) left out because 5ths aren't needed for a chord to have it's character. When chord extensions like the 9th are used, it's very common to leave out the 5th. Not only is the 5th not needed, it both muddies-up the sound of the chord and you run out of fingers to play it.