permit vs countenance

permit and countenance both are nouns.

Word	Noun	Adjective	Verb	Adverb
permit	Yes	No	Yes	No
countenance	Yes	No	Yes	No

As verbs, permit and countenance are synonyms defined as:

Other synonyms of permit include allow, let.

As verbs, countenance is a hypernym of permit; that is, countenance is a word with a broader meaning than permit:

permit: allow the presence of or allow (an activity) without opposing or prohibiting
countenance: consent to, give permission; permit

Other hypernyms of permit include allow, let, permit.

permit (noun)	countenance (noun)
the act of giving a formal (usually written) authorization	the appearance conveyed by a person's face
large game fish; found in waters of the West Indies	the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)
a legal document giving official permission to do something	formal and explicit approval

permit (verb)	countenance (verb)
consent to, give permission; permit	consent to, give permission; permit
allow the presence of or allow (an activity) without opposing or prohibiting
make it possible through a specific action or lack of action for something to happen