Each of the letters in the word HARMONIOUS is arranged in alphabetical order. How many letters are there in the English alphabetical series between the letter that is first from the left and the one that is fourth from the right in the new letter-cluster formed?

Correct — B.
Rule: sort the letters, pick the two positions, then count the letters strictly between them.

HARMONIOUS sorted: A H I M N O O R S U (ten letters, both O's kept).
1st from the left: A (1).
4th from the right: U, S, R, O → O (15).
Between them: B to N → 15 − 1 − 1 = 13 → option (b).

Why the others are wrong

• (a)
  12 — 12 is the count between A and N (14). The 4th letter from the right is O, one place further, which adds one more letter.
• (c)
  15 — 15 is O's own alphabet position. The letters strictly between A (1) and O (15) number 15 − 1 − 1 = 13.
• (d)
  11 — 11 comes from taking the 4th letter from the left, M (13): B to L is 11 letters. The question asks for the 4th from the right, O.

Rearrange first, then locate, then count. HARMONIOUS has ten letters, and the repeated O stays twice in the sorted cluster.

Count from the end the question names: from the right, the sorted cluster reads U, S, R, O, so the 4th is O. The letters between two alphabet positions number larger − smaller − 1, because neither end is counted.

Key facts

• HARMONIOUS in alphabetical order: A, H, I, M, N, O, O, R, S, U.
• A = 1, M = 13, N = 14, O = 15 in the alphabet.
• Letters strictly between positions m and n (m < n): n − m − 1.

Common traps

• Counting the 4th letter from the left (M) and choosing 11
• Writing O's position, 15, as the number of letters between A and O

No directly related past PYQ was found.