The correct answer is option A ("It persuades readers with ethos because he has followed through on his words").
To recognize the difference between these different kinds of approaches to persuasion, you have to identify the connotations of the language used, and whether it appeals to logic (logos), emotions (pathos), or ethics (ethos).
The clear center of this excerpt is Thoreau's own attitude. He's using his own questioning of laws and his response towards them as a way of leading by example. He's attempting to convince us to take his side by displaying his own integrity and virtue of character, which indicates an appeal to ethos.
Hope this helps!