What if n=33 ? It satisfies D and E, but not C. It is multiple of 3.

It's asking for any possible values of n satisfying the given conditions. n isn't a fixed number.

only B is right
1 is not prime number
and is unable to divided by 3

n+7 is a multiple of 8
also n+7 is NOT a multiple of 6

List the multiples of 8 and corresponding "n."
Put an x next to any that are also multiples of 6, because we can't use those

multiples of 8 | n (subtract 7)
----------------------
8 ------------> 1
16 -----------> 9 - multiple of 3
24x
32 -----------> 25
40 -----------> 33
48x
56 -----------> 49
64 -----------> 57
72x
80 -----------> 73 - prime
88 -----------> 81
96x

Let's take the answer choices one at a time:
We can see n is always odd, never even. We could have deduced this anyway, since a multiple of 8 is even, and subtracting 7 will always produce an odd. Thus A is false, B is true.

For C, we can see that 73 is prime.
For D, we can see that 9 is a multiple of 3.
For E, since all values are odd, we know they will not be multiples of 4.

Thus, the correct answers are B, C, D.

You cannot use n=17 as your prime, since if n=17, 17+7 = 24, which is divisible by 6. The prompt states that n+7 is not divisible by 6. Luckily, later in the list, we see n=73 IS a prime, so the answer is still that primes are possible.