Hi Soniya. "completely" and "fully" have the same meaning when you're showing nothing is missing. For example: She had fully/completely recovered from the accident. Also "fully" used to emphasize an amount or showing to contain (hold) as much as possible. For example: The disease affects fully 30 percent of the population. (not completely) I think "fully" is more natural in your sentence. For more information direct attention to Oxford Dictionary.

well, the meaning is the same.....but grammatically drain fully makes more sense

however, on my test paper the answer is "fully". 「Decant it into a bottle, make sure to drain fully.」 :< it confused me

I would say "drain completely". Example: The lake had to be drained completely in order to find the murder weapon. fully= entirely/wholly: You should be fully finished with that work by now. completely=totally /utterly: I am completely exhausted