incomprehensible
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unintelligible
Formulated or made in such a way that one cannot understand or make sense of it; unclear or meaningless.
Er murmelte etwas Unverständliches in seinen Bart.
He muttered something unintelligible into his beard.
The word is logically built: the prefix 'un-' means 'not'. The word 'verständlich' (understandable) comes from the verb 'verstehen' (to understand). So 'unverständlich' literally means 'not understandable'.
Seine Handschrift ist so klein, sie ist fast unverständlich.
His handwriting is so small that it is almost unintelligible.
If 'unverständlich' refers to speech, writing, or sounds, it means that you cannot decode something acoustically or in terms of content. If it refers to actions or decisions, it means that you cannot understand the logic or motivation behind them.
Der Arzt sprach so schnell, dass seine Erklärung unverständlich war.
The doctor spoke so quickly that his explanation was unintelligible.
To express that you personally cannot understand something, the fixed structure 'Es ist mir unverständlich, warum/dass ...' (It is incomprehensible to me why/that ...) is often used. The person who does not understand something is in the dative.
Es ist mir unverständlich, warum er so wütend geworden ist.
It is incomprehensible to me why he got so angry.
clear
'klar' and 'unverständlich' form a simple contrast. You say 'klar' when a statement, explanation, or situation is easy to understand. You say 'unverständlich' when you do not understand something or cannot make sense of it. This can be because of poor wording, but also because of behavior that does not make sense. For learners, the important point is: 'klar' helps with understanding, while 'unverständlich' shows a problem with understanding.
Vor dem Termin ist die E-Mail für viele Kollegen unverständlich.
Before the appointment, the email is incomprehensible to many colleagues.
Die Aufgabe war klar, weil der Lehrer sie gut erklärt hat.
The task was clear because the teacher explained it well.