Hello! You didn't post any options for the detail. After looking this question up, I wasn't able to find any options online either. However, it is still answerable, so I will respond in way that will most likely help you.
Answer:
The detail that marks the introduction of the conflict is:
At the sight of their uncle and his family, the young couple were horror-stricken.
Step-by-step explanation:
Before the detail above was mentioned, the couple Sasha and Varya were all smiles and pleasantness. Notice how, at the beginning of the excerpt, Sasha even says they are having a splendid time together. Also, before the detail above, the author gave us no indication that the couple and the kids who arrived were not welcome. Quite the contrary, we are even led to believe they were expected, since the uncle says Sasha has been wanting them to visit.
It is only when they author says, "At the sight of their uncle and his family, the young couple were horror-stricken" that the reader is finally able to perceive there is something wrong. From here on, the author explains that having so many people over will certainly cause problems and inconveniences for Sasha and Varya. Therefore, we can safely say that is the detail that introduced the conflict.