The correct options are
C totally
D very
The phrase, '____ well' in the given sentence modifes the verb, 'know'. Hence, it has to be an adverb.
The adverb, 'very' means 'extremely' and is used for emphasis. The expression, 'I know very well' is an often-used one which means 'I am extremely aware'. As this word meaningfully completes the given sentence, option C is correct.
Option A: The word, 'totally' is an adverb which means, 'absolutely'. The expression, 'I know totally well' is grammatically correct. However, it is very rarely used. This option is also correct.
Option B: The word, 'absolute' is an adjective which means 'total' or 'complete'. As an adjective, it can be used to describe a noun, but not the verb, 'know'. Hence, this option is incorrect.
Option D: The adverb, 'less' means 'to a smaller extent'. The expression, 'I know less well' is not complete as it does not indicate 'less well' than what. Hence, option D is incorrect.