In this spelling question on English vocabulary, select the option that shows the correctly spelled English word among the four given choices.

Introduction / Context:
Spelling based questions check your familiarity with common English words, especially those that frequently appear in news articles, official documents, and exam passages. Being able to recognise the correct spelling quickly improves both your writing and your performance in objective tests. In this question you must identify which one of the four options is spelled correctly according to standard English usage.

Given Data / Assumptions:
• Four spellings are given: "sylabus", "encroach", "coalesse", and "adhetion". • Only one of these corresponds to a correctly spelled English word. • The question does not ask for meaning, but accurate spelling.

Concept / Approach:
The word "encroach" is a common verb meaning to gradually intrude on someone else’s territory, rights, or time. The accepted spelling is e n c r o a c h. The other options look like misspellings of real words. "Sylabus" tries to represent "syllabus"; "coalesse" is a miswritten form of "coalesce"; and "adhetion" is an incorrect version of "adhesion" or "adherence". In spelling questions, a good approach is to mentally recall the correct forms you have seen in books and reliable sources and then match them against the options.

Step-by-Step Solution:
Step 1: Look at "encroach". Check whether this matches the familiar spelling you have seen in newspapers or grammar books. It does. Step 2: Examine "sylabus". The correct word is "syllabus" with a double l and a different vowel pattern, so this option is wrong. Step 3: Consider "coalesse". The correct spelling is "coalesce" ending with s c e, not s s e, so this is incorrect. Step 4: Look at "adhetion". The standard noun is "adhesion", with s i o n, so "adhetion" is a faulty spelling. Step 5: Conclude that only "encroach" is spelled correctly.

Verification / Alternative check:
You can verify by using memory techniques. Imagine a typical sentence such as "The construction work will not encroach on the children playground." Visualising the spelling in a full sentence often helps recall. Another check is to break the word into parts: "en" plus "croach". This pattern appears consistently in dictionaries and textbooks, so it is safe to choose this option as the correct spelling.

Why Other Options Are Wrong:
"Sylabus" is missing a letter l and uses y instead of the correct double l pattern in "syllabus". "Coalesse" adds an extra s; the correct ending is c e, not s e, and the double s is not part of the standard form. "Adhetion" replaces the correct ending s i o n with t i o n and alters the base, which makes it non standard English.

Common Pitfalls:
Students sometimes rely only on how a word sounds, which leads to errors because English spelling is not always phonetic. Another common mistake is to assume that any option with double consonants must be wrong, or that the longest looking word must be correct. The safest strategy is to build a habit of reading widely and noticing exact spellings, especially of words that occur in official or academic contexts. Writing new vocabulary in a personal notebook and reviewing it periodically also strengthens memory.

Final Answer:
The correctly spelled word is encroach.