What does As he said this she could easily see that he had no doubt of a favourable answer He spoke of apprehension and anxiety but his countenance expressed real secruity mean?

Answer 1

Elizabeth realizes that Mr. Darcy, despite the insulting content of his proposal, believes that she will accept his offer of marriage no matter how he phrases it ("As he said this, she could easily see that he had no doubt of a favourable answer").

Mr. Darcy also seems to be using some conventional language of love/proposals where the man expresses fear that the woman will not deem him worthy enough to marry ("He spoke of apprehension and anxiety..."). However, the enormous difference in their wealth and social status means that Mr. Darcy believes no woman in Elizabeth's position would possibly refuse ("...but his countenance expressed real security") And, to be fair to Mr. Darcy, he thinks Elizabeth has been aware of his feelings and intentionally flirting with him, another reason for his security in being accepted.

This passage communicates Elizabeth's disgust with Mr. Darcy's perceived (and actual) pride, since his "real security" is in fact unfounded; Elizabeth at this point despises Mr. Darcy and has no intention of accepting his proposal.

Answer 2

The speaker displayed confidence and certainty in receiving a positive response despite mentioning feelings of worry and fear. His facial expression revealed genuine assurance and peace of mind in the situation.