choose the correct adjective permit us to introduce ourselves said the thin man, flourishing his hat gracefully

I don't know what you mean by "the correct adjective"? There is only one adjective.

The one adjective is 'thin.'

Explanation:

- "a nonrestrictive clause functions as a modifier to a noun (that is an object, person or concept). these clauses can be described by the following three options: it is set off by comas, it contains a subject and a verbs and it adds nonessential information to the sentence.

for example, in "here is bill gates, who confounded microsoft software company" we can identify "who confounded microsoft software company" as a nonrestrictive clause modifying the noun bill gates. this clause can be describes as a nonrestrictive clause because it is separated by a comma, it adds nonessential information to identify who bill gates is and it must contain both a subject (who) and a verb (confounded)."