Think of a box with 4 particles a, b, c and d. If every particle is on the left side of the box, then there is only 1 way to divide them up. [(a, b, c, d), ()]

If there are 2 particles on the left side of the box and 2 particles on the right side of the box, then there are 6 ways to divide them up:

[(a, b), (c, d)]
[(a, c), (b, d)]
[(a, d), (b, c)]
[(b, c), (a, d)]
[(b, d), (a, c)]
[(c, d), (a, b)]

In total you've got 16 possible arrangements, the 2-2 state has the "highest" entropy because you're more likely to end up with the one that takes up 6/16 arrangements.