In the following question, out of the four alternatives, select the alternative which is the best one-word substitute for the phrase: That which cannot be put out or extinguished.

Introduction / Context:
This vocabulary question asks for a one word substitute for the description that which cannot be put out or extinguished. The phrase is often used in relation to flames, lights or even abstract things like hope and spirit. The correct answer should reflect the idea that something cannot be extinguished, that is, it continues to burn or exist.

Given Data / Assumptions:
- The descriptive phrase is: That which cannot be put out. - Options are Illusion, Indigenous, Incentive and Inextinguishable. - We are looking for an adjective that expresses impossibility of extinguishing. - The prefix in often signals negation in English.

Concept / Approach:
The verb extinguish means to put out a fire or light, or to bring something to an end. By adding a negative prefix and appropriate adjective ending, we obtain inextinguishable, meaning incapable of being extinguished. The other options belong to completely different semantic fields: illusion relates to false perception, indigenous refers to something native to a place and incentive means a motive or encouragement. Only inextinguishable directly encodes the idea of not being able to be put out.

Step-by-Step Solution:
Step 1: Recognise the core verb extinguish in the phrase be put out. We need an adjective that negates this capability. Step 2: Check option D, Inextinguishable. It is formed from extinguish with the prefix in and suffix able, meaning not capable of being extinguished. Step 3: Verify that this word is used in contexts like inextinguishable flame or inextinguishable hope, which match the description. Step 4: Compare other options: Illusion is a false idea or perception, Indigenous describes origin, and Incentive refers to a reason to act. None of these link to the idea of being put out. Step 5: Conclude that Inextinguishable is the only option that corresponds directly to the given phrase.

Verification / Alternative check:
Consider the literal image of a lamp or fire. If it cannot be put out, we might call it an everlasting or inextinguishable flame. In literature and speeches, people also talk about inextinguishable faith or inextinguishable love. These uses confirm that inextinguishable is the standard adjective for that which cannot be extinguished. The stem extinguish provides a clear link between the phrase and the one word answer.

Why Other Options Are Wrong:
Option A: Illusion describes a deceptive appearance or false belief and has nothing to do with extinguishing. Option B: Indigenous refers to something native to a region and does not match the given description. Option C: Incentive means a stimulus or motive, often financial, and again bears no relation to the idea of putting out a flame.

Common Pitfalls:
Most candidates will find this question straightforward, but some may be distracted by the similar prefixes in indigenous and incentive and choose based on familiarity rather than meaning. To avoid such errors, always connect the descriptive phrase to a root word you know, in this case extinguish, and then look for the correct negative form built from that root.

Final Answer:
The appropriate one word substitute is Inextinguishable, so option D is correct.