half dozen vs six

half dozen is not a noun while six is a noun.

Word	Noun	Adjective	Verb	Adverb
half dozen	No	Yes	No	No
six	Yes	Yes	No	No

As adjectives, half dozen and six are synonyms defined as:

half dozen and six: denoting a quantity consisting of six items or units

Other synonyms of half dozen include 6, half-dozen, vi.

half dozen (noun)	six (noun)
	a playing card or domino or die whose upward face shows six pips
	the cardinal number that is the sum of five and one

half dozen (adjective)	six (adjective)
denoting a quantity consisting of six items or units	denoting a quantity consisting of six items or units