The personality trait that would make Dickon feel at home at Buckingham Palace or at the bottom of a coal mine is that he is very likable.
It is mention trough the book that he has a strange ability to captivate everyone human or not since his ability also applies to animals, everywhere Dickon goes everyone just fell under his spell and find him lovable. We can see the quotation that says :
There really was a sort of Magic about Dickon, as Mary always privately believed. When Mr. Roach heard his name he smiled quite leniently.
“He’d be at home in Buckingham Palace or at the bottom of a coal mine,” he said. “And yet it’s not impudence, either. He’s just fine, is that lad.”
Let us dissect each sentence to tell which of these does not follow the rules for subject-verb agreement.
A.) The subject is 'each of the students' while the verb is 'is'. More particularly, the verb refers to 'each' which is singular. So, this is correct.
B.) The subject is 'student' while the verb is 'were'. The word 'were' is the paste tense of are which is used for a plural subject. But since student is singular, then the verb should have been 'was'. So, this is incorrect.
C.) The subject is 'my dog and my cat' which pertains to two nouns, thus it is plural. It agrees with its plural verb 'are'.
D.) The subject is 'Tom' while the verb is 'does'. Both are intended for singular use. So, this is correct.
Therefore, the answer to this is letter B.