half-dozen vs 6

half-dozen is not a noun while 6 is a noun.

Word	Noun	Adjective	Verb	Adverb
half-dozen	No	Yes	No	No
6	Yes	Yes	No	No

As adjectives, half-dozen and 6 are synonyms defined as:

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

half-dozen (noun)	6 (noun)
	the cardinal number that is the sum of five and one

half-dozen (adjective)	6 (adjective)
denoting a quantity consisting of six items or units	denoting a quantity consisting of six items or units