Answer:
The correct completion for the first sentence is:
B. stayed
So the complete sentence would be: "I know I promised to go with you, but I am not feeling very good. Would you mind staying home?"
For the second sentence, the correct completion is:
D. it is necessary that you do not do it (so don't do it)
So the complete sentence would be: "If I stay, we must be very quiet. We mustn't make any noise."