Вкаких случаях пишутся слова many и much ?

Вопросительные предложения

How much (how much = сколько) ... + неисчисляемые существительные

Например:
How much sugar do you take in your coffee?
Сколько сахара ты кладешь в кофе?

How much money do you want for this?
Сколько (денег) ты за это хочешь?

Do you have much work to do?
У тебя много работы?

How many (how many = сколько) ... + исчисляемые существительные

Например:
How many students are there in each class?
Сколько учеников в каждом классе?

How many people are you expecting?
Сколько человек ты ожидаешь?

Отрицательные предложения

В отрицательных предложениях конструкции Not Much и Not Many обычно переводятся как "мало", "немного".

Например:
He doesn't earn much money (существительное money - неисчисляемое).
Он зарабатывает мало (= немного) денег.

Not many people have heard of her (существительное people - исчисляемое).
Немногие о ней слышали.

Barbara doesn't have many friends.
У Барбары мало (= не много) друзей.

Many-если можно почитать по- штучно(помидор,карандаш,стул и т.д.),а much когда предмет нельзя посчитать(молоко,вода,свет и т.д.)

Nowadays the theatre is less popular than the cinema. due to the popularity of television and the since appearance of video, theatre has lost a great deal of its attraction. besides, theatre tickets are very expensive, especially in good theatres. so we can say that a visit to a famous theatre has become a luxury. still, the theatre is an inseparable part of the intellectual life of any country. we can even say that the theatre as an art reflects the state of society and of the mind of the nation. in every country theatre has its own history, traditions and peculiarities. there are a lot of theatres in russia and some of them are popular all over the world. in moscow theatre-goers try not to miss the first nights at the vakhtangov, sovremennik, or khudozhestvenny (art) theatres. st. petersburg also has a variety of theatres, which meet all the tastes. lovers of classic music never miss a chance to visit the philharmonic society hall. opera and ballet lovers can go to mariinsky opera house and maly opera house. those who are fond of drama visit the bolshoi drama theatre, alexandrinsky theatre, open theatre and many others. many new theatres and studios have appeared during the last five or ten years. many theatres are famous for theirexcellent company, sets and great directors. i'm not a regular theatre-goer, but sometimes i like to go and see an interesting performance. one of my favourite theatres is the bolshoi drama theatre. it is so not only because of it

1. I can’t remember …seeing him before (to see). 
2. The machine needs cleaning… (to clean). 
3. She is angry at … for sending (to send). ??? 
4. You should avoid breaking… rules (to break). 
5. She entered the office without  noticing… (to notice). 
6. I am sorry for …disturbing you (to disturb). 
7. We can’t excuse their not …answering our invitation (to answer). 
8. The cat was punished for …breaking the cup (to break) 
9. The cat was afraid of  punishment (punishing)… and hid itself under the sofa. (to punish). 
10. After looking… through and  marking… the student’s papers, the teacher handed them back. (to look),(to mark).