Each of the letters in the word ‘DARKEN’ is arranged in the English alphabetical order.

How many letters are there in the English alphabetical series between the letter which is second from the left end and the one which is third from the right end in the new letter-cluster thus formed?

Let's solve the problem step-by-step.

Step 1: Arrange the letters of the word 'DARKEN' in English alphabetical order.
The given word is DARKEN. The letters in this word are: D, A, R, K, E, N.
Let us find their positions in the standard English alphabet:
A = 1, D = 4, E = 5, K = 11, N = 14, R = 18.
Arranging these letters in ascending alphabetical order gives us the new letter-cluster:
A, D, E, K, N, R

Step 2: Identify the specified letters in the new letter-cluster.
- The letter which is second from the left end: In the sequence A, D, E, K, N, R, the second letter from the left is D.
- The letter which is third from the right end: In the sequence A, D, E, K, N, R, counting from the right (R is 1st, N is 2nd, K is 3rd), the third letter from the right is K.

Step 3: Find the number of letters between D and K in the English alphabetical series.
The English alphabetical series between D and K is:
E, F, G, H, I, J
Let's count these letters:
1. E
2. F
3. G
4. H
5. I
6. J
There are exactly 6 letters between D and K.

Therefore, the correct option is Six.