eigenhändig
personally
Carried out personally and without the help of other people; done with one's own hands.
Der Künstler hat jeden Druck eigenhändig signiert.
The artist personally signed every print.

personally / by one's own hand
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personally
Carried out personally and without the help of other people; done with one's own hands.
Der Künstler hat jeden Druck eigenhändig signiert.
The artist personally signed every print.

The word is made up of 'eigen' (own) and 'Hand' (hand). So it literally means 'with one's own hand' and emphasizes that an action is carried out personally and without outside help.
Der berühmte Autor schreibt alle seine Romane noch eigenhändig auf Papier.
The famous author still writes all his novels personally on paper.
'Eigenhändig' (personally/by one's own hand) is usually used as an adverb and then remains unchanged after the verb. It describes the manner of the action.
Sie hat den Kuchen für die Feier eigenhändig gebacken.
She personally baked the cake for the celebration.
Common verbs combined with 'eigenhändig' (personally/by one's own hand) are 'unterschreiben' (to sign), 'schreiben' (to write), 'bauen' (to build), 'reparieren' (to repair), or 'zubereiten' (to prepare). It is often about actions that have a personal touch or legal validity.
Das Testament muss vom Verfasser eigenhändig unterschrieben werden.
The will must be signed personally by the author.
oneself / even
'selbst' and 'eigenhändig' can both mean that someone does something personally and does not have it done by someone else. 'selbst' is more general: it can refer to any personal action, for example calling, deciding, or signing. 'eigenhändig' is more specific and emphasizes that someone carried something out with their own hands or without outside help. That is why 'eigenhändig' is especially suitable for writing, building, repairing, or signing. Learners confuse the words because both express personal execution, but 'eigenhändig' is narrower and more concrete.

Nach dem Umzug hat Mehmet den kleinen Tisch eigenhändig repariert.
After the move, Mehmet repaired the small table himself.
Bei der Bewerbung muss man das Formular selbst ausfüllen.
For the application, you have to fill out the form yourself.