These types of permutation questions can sometimes be confusing, so you might find that a "visual component" will help you to stay organized and get to the correct answer.
In this question, we have to place 4 players at 4 corners of a diamond (although you could just as easily have a question that places them at equidistant spots on a circle).
If we were placing those 4 players in a straight line, then the number of possibilities would be a simple calculation:
(4)(3)(2)(1) = 24
HOWEVER, since we're told that we can count an option ONLY if the relative positions of the players differ.
This means that the following 4 options are all the SAME thing:
The first option (ABCD) is simply "revolved" around the diamond, so the relative positions of the players are NOT different.
Mathematically, we have to divide 24 by 4, so that remove all of the "duplicates"
All in all, this a relatively rare issue on the GMAT (you probably won't see it; even if you aced the Quant section, you still probably wouldn't see it).
GMAT assassins aren't born, they're made,
Official Guide 2016 Question Breakdown:
GMAT Club Verified Reviews for EMPOWERgmat & Special Discount
EMPOWERgmat Podcast - A Wild Secret About The GMAT Algorithm