One is expected to abide and respect the law of one's country.

A. abide and respect the law of one's
B. abide by and respect the law of their
C. abide by and respect the law of his
D. respect and abide by the law of one's
E. have respect for and abide by the law of one's

Since the subject of the given sentence is One, any possessive form of that subject must be one's. In other words, the arbitrary use of the possessive adjectives their and his would not be considered acceptable in the GMAT. This means that you can discard B and C.

The verb in A, to abide means to tolerate, to bear, as in the sentence Some people can't abide the smell of garlic. But it makes little sense to say that One is expected to tolerate and respect a law: how, indeed, does one tolerate a law? What is needed here is a synonym for the other verb in the sentence, respect. So you can now discard A.

Both D and E use abide by, which means, more or less, obey. This makes sense. One might well abide by a law. A democratic government must abide by the terms of a constitution.

E, however, introduces a change of meaning. One can have respect for a person or for laws, but this is simply a feeling. One might feel that a law is powerful or beneficial, and so feel respect for it. But this is not what the sentence is getting at. We want a verb to match and reinforce abide by. This verb is simply to respect, which means to submit to or obey So you can discard E.

D is the only remaining option. Here, you have a succinct and meaningful statment: one must both respect (i.e. submit to) and abide by (i.e. obey) the law of one's country. This is therefore the correct answer.