Решение:
- He went on (type) his report until the morning. - typing
- After Jane had completed her Italian course she went on (improve) her Spanish. - to improve
- Why don't you try (drink) not so much coffee? - drinking
- I tried (open) the door but I couldn't. - to open
- We regret (tell) you that you have not been selected for the team. - to tell
- Sam regretted (tell) his best friend lies. - telling
- Children had been playing for quite a while before they stopped (have) dinner. - to have
- She's been having trouble sleeping lately so she's (have) coffee in the afternoon. - having
- I hate (bother) you, but may I ask you to help me? - to bother / bothering
- I hate (cause) you so much trouble. - to cause / causing
- I will never forget (meet) you for the first time. - meeting
- Tom forgot (buy) milk. - to buy
Ответ: 1. typing; 2. to improve; 3. drinking; 4. to open; 5. to tell; 6. telling; 7. to have; 8. having; 9. to bother / bothering; 10. to cause / causing; 11. meeting; 12. to buy.