Per biblehub.com the word diatarassó, rendered here as greatly troubled, occurs just once in the text.
diatarassó: to agitate greatly
Original Word: διαταράσσω
Part of Speech: Verb
Phonetic Spelling: (dee-at-ar-as'-so)
Definition: to agitate greatly
Usage: I trouble greatly, agitate.
That Mary was greatly troubled by the angel’s praise is indicative of her humility. Mary’s reaction reveals much about her character and contrasts with that of Zechariah’s just a few verses earlier.
And there appeared unto him an angel of the Lord standing on the right
side of the altar of incense. 12 And when Zacharias saw him, he was
troubled, and fear fell upon him. – Lk 1:11-12 KJV
And the angel came in unto her, and said, Hail, thou that art highly
favoured, the Lord is with thee: blessed art thou among women. 29 And
when she saw him, she was troubled at his saying, and cast in her
mind what manner of salutation this should be. – Lk 1:28-29
Whereas Zechariah was troubled (tarassó) at the sight of the angel, Mary was "greatly troubled" (diatarassó) by his words/greeting. Mary’s reaction is consistent with other passages in the text that show her to be a quietly observant and introspective person.
And all they that heard it wondered at those things which were told
them by the shepherds. 19 But Mary kept all these things, and pondered
them in her heart. – Luke 2:18-19
And he went down with them, and
came to Nazareth, and was subject unto them: but his mother kept all
these sayings in her heart. – Luke 2:51
Mary was troubled by and attentive to the words of the angel. She clearly understood that his words constituted a message from God. Both her humility and attentiveness to God’s word are evident in her answer.
And Mary said, Behold the handmaid of the Lord; be it unto me
according to thy word. – Luke 1:38