endgültig
final
Concluding, definitive, and no longer changeable. It describes a state or decision that is final.
Nach langer Diskussion trafen sie eine endgültige Entscheidung.
After a long discussion, they made a final decision.

final
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final
Concluding, definitive, and no longer changeable. It describes a state or decision that is final.
Nach langer Diskussion trafen sie eine endgültige Entscheidung.
After a long discussion, they made a final decision.

The word is made up of 'Ende' (end) and 'gültig' (valid). So it literally means that something is valid until the end and therefore can no longer be changed.
Das ist mein endgültiges Angebot.
That is my final offer.
'Endgültig' (final/finally) can stand as an adjective before a noun or as an adverb that refers to the verb. As an adverb, it describes that an action is completed finally.
Das ist die endgültige Version des Dokuments.
This is the final version of the document.
In its main meaning, 'endgültig' (final) is often combined with nouns that express a conclusion or a fixed decision. Typical examples are: 'endgültige Entscheidung' (final decision), 'endgültiges Ergebnis' (final result), or 'endgültiger Abschied' (final farewell).
Das endgültige Ergebnis der Wahl wird morgen bekannt gegeben.
The final result of the election will be announced tomorrow.
As an adverb, 'endgültig' (finally) often expresses impatience or determination and emphasizes that a limit has been reached. In this use, it often stands at the beginning of the sentence or is emphasized especially strongly.
Jetzt reicht es aber endgültig!
Now that's finally enough!
last
'letzt' and 'endgültig' both have to do with an ending. 'letzt' describes something that comes at the end of a sequence, for example 'der letzte Termin' (the last appointment) or 'die letzte Frage' (the last question). 'endgültig' describes something that has been decided and will no longer be changed. They can be confused because a final step can sometimes also feel definitive. But not everything that comes last is automatically final. 'letzt' asks: Where does something stand in the sequence? 'endgültig' asks: Can it still be changed?

Nach dem Gespräch ist die Entscheidung endgültig.
After the conversation, the decision is final.
Vor der Prüfung stellt ihr noch eine letzte Frage.
Before the exam, she asks one last question.