Answer:
1. evinced = D. to show
If you read the sentence carefully, you can infer the meaning of the word in bold letters just based on the context and the surrounding words. So, it says that 'she evinced so much intelligence,' meaning that she showed it, exhibited it, it was made obvious to other people.
2. forbore = C. to refrain from
The meaning of this word can also be deduced based on the context. So, in the sentence, it says that this person was able to tell anything to that woman, except for the fact that her darling looked sick. So he refrained from telling her that, meaning that he stopped himself.
3. eking = A. to make a supply last by economy
If you were unsure about this one, you could have matched every other option and then match this one to the remaining one. :) However, you can see in the sentence that this woman did something in order to help the cook and her children from having to live solely on gravy and other scrapings.
4. disencumber = B. to free from
In this sentence, you can see that the narrator would like one particular man to perish from the face of the Earth. She considers him plague, and would like to rid the planet from him. Thus, disencumber in this context means to free something from something bad