For this question, we can quickly test values to eliminate answer choices.

For example, let's test \(n = 1\)
Wait a second. Why am I testing \(n = 1\), when the question clearly tells us that \(n\) is greater than 6?
In my opinion, the test makers added that proviso (n > 6) so that students don't have to know whether 0 is divisible by 3.
What really matters here is that all integers fall into three categories when it comes to divisibility by 3:
- the number is divisible by 3
- the number leaves a remainder of 1 when divided by 3
- the number leaves a remainder of 2 when divided by 3
The first number I'm testing (\(n = 1\)) leaves a remainder of 1 when divided by 3. As you'll see, when I plug that value into answer choice A, the result is divisible by 3. You'll find that if you take ANY integer that leaves a remainder of 1 when divided by 3 and plug it in to answer choice A, the result will always be divisible by 3.
So, rather than test large values of n, I'm going to save some time and test small values (even though I'm breaking the restriction that n > 6)

A. \(1 (1+1) (1-4)=-6\) Divisible by 3
B. \(1 (1+2) (1-1)=0\) Divisible by 3
C. \(1 (1+3) (1-5)=-16\) NOT divisible by 3. Eliminate.
D. \(1 (1+4) (1-2)=-5\) NOT divisible by 3. Eliminate.
E. \(1 (1+5) (1-6)=-30\) Divisible by 3

Now let's test \(n = 2\)
A. \(2 (2+1) (2-4)=-12\) Divisible by 3
B. \(2 (2+2) (2-1)=8\) NOT divisible by 3. Eliminate.
E. \(2 (2+5) (2-6)=-56\) NOT divisible by 3. Eliminate.

Answer: A