handgreiflich
violent
Using physical violence; hitting, pushing, or otherwise physically attacking someone.
Nach einem lauten Streit wurde einer der Männer handgreiflich.
After a loud argument, one of the men became violent.

violent / tangible
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violent
Using physical violence; hitting, pushing, or otherwise physically attacking someone.
Nach einem lauten Streit wurde einer der Männer handgreiflich.
After a loud argument, one of the men became violent.

The adjective is derived from 'Hand' (hand) and 'greifen' (to grasp). The ending '-lich' makes it an adjective. The literal idea is something that you can grasp or touch with your hand, which explains both the physical and the figurative meaning.
Seine Wut war fast handgreiflich, so wütend war er.
His anger was almost tangible, that was how angry he was.
In the meaning 'physically violent', 'handgreiflich' (violent) is very often combined with the verb 'werden' (to become). The phrase 'handgreiflich werden' means to start using physical violence.
Die Diskussion wurde so hitzig, dass er beinahe handgreiflich geworden wäre.
The discussion became so heated that he almost became violent.
The meaning 'offensichtlich' (obvious) or 'fassbar' (tangible/graspable) is rare today and is perceived as elevated or becoming dated. You are more likely to find it in older literature or in very formal language.
Der Vorteil dieser Methode war ein handgreiflicher Beweis für ihre Effektivität.
The advantage of this method was tangible proof of its effectiveness.
You can easily distinguish the two meanings: If 'handgreiflich' (violent/tangible) refers to a person's behavior in a conflict, it means 'gewalttätig' (violent). If it describes a thing, a piece of evidence, or an advantage, it means 'offensichtlich' (obvious) or 'konkret' (concrete).
Er wurde gegenüber dem Polizisten handgreiflich.
He became violent toward the police officer.
clear / clearly
'deutlich' and 'handgreiflich' can both mean that something is clearly recognizable. In this sense, however, 'deutlich' is the normal word. 'handgreiflich' sounds elevated and somewhat old-fashioned in this meaning. In everyday language, 'handgreiflich' much more often means that someone becomes physically violent. For this reason, 'deutlich' is almost always the safer choice if you simply mean 'clearly recognizable'.

Nach der langen Diskussion wurden die Folgen der Entscheidung handgreiflich.
After the long discussion, the consequences of the decision became tangible.
Vor dem Termin erklärt die Kundin deutlich, welches Problem ihr Computer hat.
Before the appointment, the customer clearly explains what problem her computer has.