sixth vs 6th

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

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

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

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

sixth (noun)	6th (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

sixth (adjective)	6th (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