6 vs half dozen

6 is a noun but half dozen is not a noun.

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

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

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

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

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