The correct sentence that shows the verb agreeing with the subject is:
c) either the father or the children are good
However, to be grammatically correct, it should actually be: "Either the father or the children are good."
The other sentences have subject-verb agreement errors:
a) should be "some of the cake was eaten last night" (since "some" refers to an uncountable noun "cake").
b) should be "each of you has to attend the graduation" (as "each" is singular).
d) should be "every chair and table is donated to MP" (as "every" is treated as singular).