The question asks us to find the word that is closest in meaning to "Inexplicable" from the given options. To do this, we need to understand the precise meaning of "Inexplicable" and then compare it with the definitions of each option.

Inexplicable Definition

The word "Inexplicable" is derived from 'in-' (meaning 'not') and 'explicable' (meaning 'able to be explained'). Therefore, "Inexplicable" refers to something that cannot be explained or accounted for. It implies a mystery or a situation where the reasons or causes are unknown and cannot be logically presented or understood.

Option Meanings

Let's analyze each of the provided options:

• Incomprehensible: This word combines the prefix 'in-' (not) with 'comprehensible' (able to be understood). Thus, "Incomprehensible" means something that is not able to be understood or grasped. If something cannot be explained, it often means it cannot be fully understood.
• Indelible: This term refers to something that cannot be removed or erased. For example, an indelible mark or an indelible memory. It relates to permanence, not to the ability to be explained or understood.
• Inextricable: This word describes something from which it is impossible to escape or disentangle. For instance, an inextricable problem or an inextricable link between two concepts. It implies a complex, often unavoidable connection, rather than a lack of explanation.
• Infallible: This means incapable of making mistakes or being wrong. It is commonly used to describe a person or a system that is always correct and never fails. This term relates to accuracy and perfection, not directly to the concept of being explainable or understandable.

Meaning Comparison

When something is Inexplicable, it means that its cause, reason, or nature cannot be clarified or put into understandable terms. This inherent inability to explain often directly leads to the inability to understand it. If you cannot explain why an event occurred, you are likely unable to fully comprehend it.

Consider the relationship:

• An Inexplicable phenomenon (something that cannot be explained) often becomes Incomprehensible (something that cannot be understood). The lack of explanation directly impedes understanding.
• While an indelible mark is permanent, its permanence can often be explained (e.g., "The indelible ink is permanent due to its chemical bonding properties.").
• An inextricable problem might be complex, but its intricate nature can still be explained (e.g., "The inextricable link between economic policy and social welfare can be explained through their interdependent effects.").
• An infallible decision can be explained by the process or wisdom that led to it (e.g., "Her infallible judgment is explained by years of experience and meticulous research.").

Therefore, out of all the options, "Incomprehensible" is the closest in meaning to "Inexplicable" because both terms denote a state where something cannot be grasped or made sense of, with the former often being a consequence of the latter.