6th vs sixth

6th is not a noun while sixth is a noun.

Word	Noun	Adjective	Verb	Adverb
6th	No	Yes	No	No
sixth	Yes	Yes	No	No

As adjectives, 6th and sixth are synonyms defined as:

6th and sixth: coming next after the fifth and just before the seventh in position

6th (noun)	sixth (noun)
	the musical interval between one note and another six notes away from it
	one part in six equal parts
	position six in a countable series of things

6th (adjective)	sixth (adjective)
coming next after the fifth and just before the seventh in position	coming next after the fifth and just before the seventh in position