It is a normal 4 : 3 polyrhythm, but each part is shifted in time by half a beat - so the 4 is shifted in time by an eighth of the measure, and the 3 part is shifted by a sixth of the measure, to create this syncopated feel (i.e. played "off the beat").
To make this rhythm I set the first two parts to play 8 beats to a measure, and the second two parts to play six beats to a measure.
Then, I skipped alternate beats by hand in the first and third part. In second and fourth part skipped all except one beat to add the extra emphasis in each one.