Hello native English speakers.
1. Though we may detest him, we must acknowledge his greatness.
2. No matter how much we detest him, we must acknowledge his greatness.
3. Detest him as we may, we must acknowledge his greatness.
4. Detest we him as we may, we must acknowledge his greatness.

Question A: Which is grammatically correct?
I guess all are grammatically correct except sentence 4.
However, my grammar book states that sentence 4 is also correct. Furthermore, it points out that the concessive adverbial structure introduced by "as" can also form a complex sentence containing an object clause. When the subject of the main clause and the (object) clause are both the same personal pronoun, the subject of the main clause is often omitted.

Question B: Look and sentences 4 (4. Detest we him as we may, we must acknowledge his greatness.),
here, my question is: Notice the first "we" in sentence 4, which , according to my grammar book, indicates that the first"we" here is the subject of the main clause. Then what is the object clause here?

Question

Hello native English speakers.
1.  Though we may detest him, we must acknowledge his greatness.
2.  No matter how much we detest him, we must acknowledge his greatness.
3.  Detest him as we may,   we must acknowledge his greatness.
4.  Detest we  him as we may,   we must acknowledge his greatness.

Question A:  Which is grammatically  correct?
I guess all are grammatically correct except sentence 4.
However, my grammar book states that  sentence 4 is also correct. Furthermore, it points out that the concessive adverbial structure introduced by "as" can also form a complex sentence containing an object clause. When the subject of the main clause and the (object) clause are both the same personal pronoun, the subject of the main clause is often omitted.

Question B:    Look and sentences 4  (4.  Detest we him as we may,   we must acknowledge his greatness.),
here,  my question is: Notice the first "we" in sentence 4,  which , according to my  grammar book, indicates that the first"we" here is the subject of the main clause. Then what is the object clause here?

Answer

The first three sentences are correct.

For sentence 4; this is not correct at all. "Detest him as we may," is a single concessive clause, not an object clause. The main clause is "we must acknowledge his greatness." It might be an error or misunderstanding of an outdated word order.