1. Does he enjoy (to teach, teaching)?
2. Why have you stopped? - Go on (to read, reading).
3. I decided (to spend, spending) our holidays in France.
4. The Browns want (to leave for, leaving for) Boston this week.
5. I'll always remember (to meet, meeting) you for the first time.
6. I enjoy (to travel, travelling) very much.
7. They agreed (to repair, repairing) the car as quickly as possible.
8. I can't help (to think, thinking) about that awful accident.
9. Avoid (to overeat, overeating) and you'll feel better soon.
10. My car needs a service badly, and Tom offered (to help, helping) me with it.
11. I really must stop (to smoke, smoking).
12. All parts of London seem (to belong, belonging) to different towns and epochs.
13. Would you mind (to close, closing) the front door?
14. Although I was in a hurry, I stopped (to talk, talking) to him.
15. You should remember (to phone, phoning) him. He'll be at home.
16. I offered (to go, going) by bus or by train.
17. When we had finished (to eat, eating), the waiter brought the bill.
18. If possible, give up (to smoke, smoking), at least for a time.
19. I avoid (to worry, worrying) people about things of no importance.
20. He kept (to think, thinking) over what he had felt that night.
21. She looked up and burst out (to laugh, laughing).
22. She didn't mind (to share, sharing) her cabin with another woman.
23. He didn't feel like (to make, making) jokes any longer.
24. Do you remember (to meet, meeting) Sam at the cinema last year?
25. They suggested (to postpone, postponing) the match to the following week.
26. He denied (to tell, telling) lies.
27. I look forward (to seeing, to see) you at the party.
28. He stopped (to wear, wearing) ties years ago.
29. I stopped (to tie, tying) up my shoe lace.
30. They were looking forward (to go, to going) on holiday.
31. He admitted (to lie, lying) to the police.
32. They tried (to help, helping) but it was no use.
33. The door appears (to be locked, locking).
34. Jack insisted on (to catch, catching) an early flight.
35. I suggested (to take, taking) the train.
36. He didn't enjoy (talking, to talk) very much.
37. He didn't seem (to be, being) particularly talented.
38. He avoids (to go, going) to noisy bars.
39. Is there anything in that new magazine worth (to read, reading)?
40. I hope (to get, getting) there.

1. Does he enjoy (to teach, teaching)?
Answer: He enjoys teaching.

To determine whether we should use the infinitive form "to teach" or the gerund form "teaching," we need to consider the verb "enjoy" and its pattern. In this case, "enjoy" is followed by the gerund form of the verb (V+ing), so we use "teaching."

2. Why have you stopped? - Go on (to read, reading).
Answer: Go on reading.

In this case, "go on" is followed by the gerund form of the verb (V+ing), so we use "reading."

3. I decided (to spend, spending) our holidays in France.
Answer: I decided to spend our holidays in France.

In this case, "decided" is followed by the infinitive form of the verb (to + base form of the verb), so we use "to spend."

4. The Browns want (to leave for, leaving for) Boston this week.
Answer: The Browns want to leave for Boston this week.

In this case, "want" is followed by the infinitive form of the verb (to + base form of the verb), so we use "to leave."

5. I'll always remember (to meet, meeting) you for the first time.
Answer: I'll always remember meeting you for the first time.

In this case, "remember" is followed by the gerund form of the verb (V+ing), so we use "meeting."

6. I enjoy (to travel, travelling) very much.
Answer: I enjoy traveling very much.

In this case, "enjoy" is followed by the gerund form of the verb (V+ing), so we use "traveling."

7. They agreed (to repair, repairing) the car as quickly as possible.
Answer: They agreed to repair the car as quickly as possible.

In this case, "agreed" is followed by the infinitive form of the verb (to + base form of the verb), so we use "to repair."

8. I can't help (to think, thinking) about that awful accident.
Answer: I can't help thinking about that awful accident.

In this case, "can't help" is followed by the gerund form of the verb (V+ing), so we use "thinking."

9. Avoid (to overeat, overeating) and you'll feel better soon.
Answer: Avoid overeating and you'll feel better soon.

In this case, "avoid" is followed by the gerund form of the verb (V+ing), so we use "overeating."

10. My car needs a service badly, and Tom offered (to help, helping) me with it.
Answer: My car needs a service badly, and Tom offered to help me with it.

In this case, "offered" is followed by the infinitive form of the verb (to + base form of the verb), so we use "to help."

(Note: In some cases, both the infinitive and gerund forms can be used, but the choice depends on the intended meaning and context.)

I hope this detailed and explanatory answer helps you understand the correct usage of the verbs in each sentence.