Neither is considered plural and either is considered singular. You just have to memorize how either and neither are used.

Both A and B have plural subjects and would take a plural verb.

Source:

Harbrace College Handbook, Revised 13th Edition.

Page 86-87 (for coverage of NEITHER and EITHER. The other two are obvious.)

For instance, the book offers these two sentences as correct:

“Neither the basket nor the apples were expensive.” (p.86)

“Either of them is willing to shovel the driveway.” (p.87)

BE CAREFUL: either and neither follow one rule (always singular) and either-or and neither-nor follow a different rule. Read your rules and examples carefully. Either and neither usually have prepositional phrases after them; remove those phrases since they don’t contain the subject

Ex. Neither of the boys is here.

Ex. Neither the boys nor Mary is here.

Same goes for either.

Ex. Either of the boys needs help.

Ex. Either the girls or the boy is right.

A. Jennifer and her class (class is plural)

B. The twins (you are talking about two people)

D. Children (plural)

But in answer C, you there are two single people that are being referred to, so you can you use has.

If you said, “Either the children or Samuel”, then you could use “has.” (neither/nor and either/or are used as conjunctions in these examples.)