Thank you for your help.

One more time, I'd like to post the structure 'prefer to'

1. I prefer him to her.

2. I prefer Ted to Jacob.

3. I prefer table tennis to soccer.

4. I prefer reading books to playing soccer.

5. I prefer to read books rather than (to) play soccer.

6. I prefer cooking alone.

7. I prefer to cook alone.

8. I like cooking alone better.

9. I like to cook alone better.

10. I would prefer cooking/ to cook

11. I would rather cook alone.

12. I would rather stay at home than play soccer outside.

(Are they all grammatical?)

All are fine, yes.

4 IS NOT GRAMMATICAL

5 IS NOT GRAMMATICAL
7 IS NOT GRAMMATICAL
9 IS NOT GRAMMATICAL
10 IS NOT GRAMMATICAL

Yes, all the sentences you have provided are grammatically correct. They all use the structure "prefer to" to express a preference for one thing over another. Here is a breakdown of each sentence:

1. "I prefer him to her." - This sentence compares two people and expresses a preference for one person over the other.

2. "I prefer Ted to Jacob." - Similar to the previous sentence, this sentence compares two people and expresses a preference for Ted over Jacob.

3. "I prefer table tennis to soccer." - This sentence compares two sports and expresses a preference for playing table tennis over soccer.

4. "I prefer reading books to playing soccer." - This sentence compares two activities and expresses a preference for reading books over playing soccer.

5. "I prefer to read books rather than play soccer." - This sentence uses the structure "prefer to" to compare two activities and express a preference for reading books instead of playing soccer.

6. "I prefer cooking alone." - This sentence expresses a preference for cooking alone.

7. "I prefer to cook alone." - Similar to the previous sentence, this sentence uses the structure "prefer to" to express a preference for cooking alone.

8. "I like cooking alone better." - This sentence uses the verb "like" instead of "prefer" but still expresses a preference for cooking alone.

9. "I like to cook alone better." - Similar to the previous sentence, this sentence uses the verb "like to" to express a preference for cooking alone.

10. "I would prefer cooking/to cook." - This sentence uses the future conditional form and expresses a hypothetical preference for cooking.

11. "I would rather cook alone." - This sentence uses the phrase "would rather" to express a strong preference for cooking alone.

12. "I would rather stay at home than play soccer outside." - This sentence uses the phrase "would rather" to express a preference for staying at home instead of playing soccer outside.