Answer:
Based on this passage, the best synonym for the word appraise is study. The correct answer is the third one.
Step-by-step explanation:
According to this passage, the general was always paying attention to what the host was doing in order to know him better, in order to figure him out. The key phrase, in order to know the meaning of the word apprise has in this context, is the one that says "whenever he looked up from his plate, he found the general studying him, appraising him narrowly". The general was looking at him closer, he was studying him.