In American English, periods ALWAYS go inside the quotation marks.
INCORRECT: Roosevelt spoke of December 7, 1941, as “a day that will live in
infamy”.
CORRECT: Roosevelt spoke of December 7, 1941, as “a day that will live in
infamy.”
Some exceptions occur when citing a direct quote:
INCORRECT: She knows she is no longer safe, saying, “I feared for my Safety in this wicked
House (28)."
CORRECT: She knows she is no longer safe, saying, “I feared for my Safety in this wicked
House” (28).
In your example, the first sentence is correct:
CORRECT: One example is, "...but the women were eager to her of her sumptuous dinner" (p. 136).
Your second sentence is not:
INCORRECT: It should say, "eager to hear of her sumptuous
dinner".
CORRECT: It should say, "eager to hear of her sumptuous
dinner."
This link (
https://www.hamilton.edu/academics/cent ... quotations) has more examples/explanations.