vollkommen
completely
Means fully, entirely, or absolutely. It is often used as an adverb to intensify an adjective or an opinion.
Das ist eine vollkommen neue Situation für uns.
This is a completely new situation for us.

complete / perfect
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completely
Means fully, entirely, or absolutely. It is often used as an adverb to intensify an adjective or an opinion.
Das ist eine vollkommen neue Situation für uns.
This is a completely new situation for us.

'Vollkommen' is made up of 'voll' (full) and the participle of 'kommen' (to come). The literal idea is that something has 'come to fullness,' meaning it is complete or perfect.
Nach dem langen Spaziergang herrschte vollkommene Stille im Haus.
After the long walk, there was perfect silence in the house.
'Vollkommen' can be used as an adverb for emphasis (meaning 1) or as a normal adjective (meaning 2). As an adverb, it is not declined; as an adjective before a noun, it is.
Ich bin mit deiner Arbeit vollkommen zufrieden.
I am completely satisfied with your work.
In its role as an adverb, 'vollkommen' often intensifies adjectives or opinions. Typical combinations are 'vollkommen richtig' (completely right), 'vollkommen falsch' (completely wrong), 'vollkommen egal' (completely irrelevant), or 'vollkommen ausreichend' (completely sufficient).
Es ist vollkommen egal, ob wir heute oder morgen anfangen.
It is completely irrelevant whether we start today or tomorrow.
In the meaning of 'perfect,' 'vollkommen' is often combined with abstract nouns, such as 'vollkommene Harmonie' (perfect harmony), 'vollkommene Stille' (perfect silence), or 'vollkommene Dunkelheit' (complete darkness).
Für einen Moment herrschte vollkommene Stille im Raum.
For a moment, there was perfect silence in the room.
whole / quite
'ganz' and 'vollkommen' can both strongly intensify a statement and mean 'completely'. 'ganz' is very common in everyday language and can be strong or somewhat weaker, depending on the sentence. 'vollkommen' sounds stronger and often a bit more formal. It fits well when something really is entirely that way, or when something is meant to be perfect and without flaws. Learners may confuse the words because both can stand before adjectives. If you want to speak simply and neutrally, 'ganz' is usually natural. If you want to emphasize very clear or perfect completeness, 'vollkommen' fits better.

Die Küche ist nach dem Putzen vollkommen sauber.
After cleaning, the kitchen is perfectly clean.
Nach der Arbeit war die Kundin ganz zufrieden mit dem neuen Vertrag.
After work, the customer was quite satisfied with the new contract.