complete / completely
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completely
Completely, entirely, without anything left over. The word is used both for material things and for abstract matters such as feelings or doubts.
Nach der langen Wanderung waren wir restlos erschöpft.
After the long hike, we were completely exhausted.
The word is made up of 'Rest' (remainder) and the ending '-los' (-less). The ending '-los' means 'without', so 'restlos' literally means 'without a remainder'.
Bitte esst den Kuchen restlos auf, damit wir nichts wegwerfen müssen.
Please eat up the cake completely so we don't have to throw anything away.
'Restlos' is often used like an adverb to intensify another word. It then means 'völlig' (totally) or 'komplett' (completely) and makes the statement stronger.
Das Konzert war schon nach wenigen Stunden restlos ausverkauft.
The concert was completely sold out after just a few hours.
Common combinations are 'restlos begeistert sein' (to be completely thrilled), 'restlos überzeugt sein' (to be completely convinced), 'etwas restlos aufklären' (to fully solve/clarify something), or 'etwas restlos aufessen' (to eat something up completely).
Die Polizei konnte den Fall restlos aufklären.
The police were able to fully solve the case.
whole / quite
'ganz' and 'restlos' can both express that something is complete. 'ganz' is more general and can have many meanings: a whole thing, complete tiredness, or even just mild emphasis. 'restlos' is more precise: it means that truly nothing is left over or that there are no doubts left. 'restlos' is often used with food, supplies, problems, or conviction. If you simply mean the whole or entirety of something, 'ganz' fits. If you want to emphasize that nothing remains, 'restlos' is more natural.
Nach der Feier war der Kuchen restlos aufgegessen.
After the party, the cake had been completely eaten.
Meine Mutter hat den ganzen Abend auf der Veranstaltung geholfen.
My mother helped at the event the whole evening.