This is the 13852nd most frequent Russian word.
обещанную
"Promised."
In this sentence, 'обещанную' is a feminine singular accusative form of the adjective 'обещанный', describing the noun 'книгу' (book).
Он вернул обещанную книгу.
He returned the promised book.
Here, 'обещанную' again takes the feminine singular accusative form describing the noun 'помощь' (help).
Она ждала обещанную помощь.
She was waiting for the promised help.
In this case, 'обещанное' is used in the neuter singular nominative form to agree with the noun 'письмо' (letter).