Answer:
B. the desire of Mr. Archer to marry May quickly
D. the party’s nervousness about meeting Countess Olenska
Explanation:
So, for the quick summary of this excerpt, May and Mr. Archer are engaged and soon to be married. They, along with Mrs. Welland, May's mother, come to visit May's grandmother, old Mrs. Mingott, the family matriarch, in order to show her the engagement ring and ask for her permission to marry as soon as possible.
Before arriving at Mrs. Mingott's, they were worried about meeting Countess Olenska, May's cousin, a woman whose behaviour and life choices weren't acceptable by the upper class of society this family belonged to.
So, we can see the conflict in nervousness about meeting the Countess, but there is also the conflict of Mr. Archer wanting to marry May as quickly as possible (the very reason the came to Mrs. Mingott).