In this English spelling question, four similar looking words are given; choose the correctly spelt word from the options below.

Introduction / Context:
This question checks your command of correct English spelling. The word in focus is hierarchy, a commonly used term in organisational and social contexts. In competitive exams, examiners often give several similar looking spellings with rearranged vowels or doubled consonants. You must identify which spelling is accepted in standard English.

Given Data / Assumptions:
We are provided with four alternatives:

• Heirrarchy
• Hierrarchy
• Hierarchy
• Heirarchy

We must choose the correctly spelt word.

Concept / Approach:
Hierarchy is the correct English word that refers to a system in which people or things are arranged according to their importance or authority. The standard spelling is h i e r a r c h y. The distractor options change the positions of vowels or introduce extra letters. A good approach is to mentally break the word into syllables and compare them with the familiar correct form, or recall how it appears in textbooks and articles.

Step-by-Step Solution:
Step 1: Recall the word hierarchy from common usage, for example organisational hierarchy or social hierarchy. Step 2: Write the mental pattern h i e r a r c h y, paying attention to the order of i and e after h and the placement of a. Step 3: Examine Heirrarchy. This has double r after hei and also misplaces the vowels, so it does not match the known pattern. Step 4: Examine Hierrarchy. Here the letter order suggests h i e r r a r c h y with double r together, which is incorrect. Step 5: Examine Hierarchy. This exactly matches the standard spelling: h i e r a r c h y, with no extra letters and vowels in the correct order. Step 6: Examine Heirarchy. This variant begins with h e i r, resembling heir, and then continues wrongly as archy. This is not the correct spelling of the word for a graded system of ranks. Step 7: Since only Hierarchy corresponds to the accepted spelling, it is the correct answer.

Verification / Alternative check:
You can quickly verify by thinking of related forms like hierarchical. In that form, we clearly see hier- and -arch, pointing back to the same spelling in hierarchy. Spell checkers in word processors also recognise hierarchy as correct and underline the other forms as mistakes. The etymology from Greek hieros (sacred) and archos (leader) is visible in the sequence hier + arch + y, again confirming the chosen spelling.

Why Other Options Are Wrong:
Heirrarchy is wrong because it adds an extra r and scrambles the vowels. Hierrarchy is wrong for the same reason: the cluster -err- is incorrect. Heirarchy is wrong because the initial hei part turns the word into something closer to heir, and the following letters do not match the standard form. None of these variants appear in dictionaries as accepted spellings of hierarchy.

Common Pitfalls:
Many learners confuse the order of i and e in hierarchy and are misled by patterns like receive or believe. Another problem is inserting extra r letters because the word sounds like it has a slight extra r sound in some accents. The safest method is to learn hierarchy visually as a whole word and reinforce it through reading and writing. Frequent exposure fixes the correct shape of the word in your memory.

Final Answer:
The correctly spelt word is Hierarchy.