six vs half a dozen

six and half a dozen both are nouns.

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

As nouns, six and half a dozen are synonyms defined as:

six and half a dozen: the cardinal number that is the sum of five and one

Other synonyms of six include 6, Captain Hicks, hexad, sestet, sextet, sextuplet, sise, sixer, VI.

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

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