1) Use the most common words.
1. There isn't much / many / a lot of coffee
2. How much / many / a lot of eggs are there?
3. There are much / many / a lot of fish.
4. Don't eat too much / many / a lot of sweets.
5. How much / many / a lot of is it?
6. Peter drinks much / many / a lot of water.
7. We didn't hear much / many / a lot of noise.
8. There aren't much / many / a lot of cars.
9. She has much / many / a lot of books.
2) Use the most common words
1. There weren't much / many / a lot of animals.
2. Is there much / many / a lot of snow?
3. I haven't got much / many / a lot of shoes.
4. It has much / many / a lot of legs.
5. They are much / many / a lot of older than me.
6. Did you watch much / many / a lot of movies?
7. Thank you very much / many / a lot of.
8. I made much / many / a lot of mistakes.
9. For how much / many / a lot of nights?

Правильные варианты:

1)

1. There isn't much coffee.
   (Кофе — неисчисляемое слово, поэтому much.)

2. How many eggs are there?
   (Яйца можно посчитать, поэтому many.)

3. There are a lot of fish.
   (Рыба здесь как количество рыб, поэтому a lot of.)

4. Don't eat too many sweets.
   (Конфеты можно посчитать, поэтому many.)

5. How much is it?
   (Цена — неисчисляемое количество денег, поэтому much.)

6. Peter drinks a lot of water.
   (Вода — неисчисляемое слово, обычно используем a lot of в утвердительных предложениях.)

7. We didn't hear much noise.
   (Шум — неисчисляемое слово, поэтому much.)

8. There aren't many cars.
   (Машины можно посчитать, поэтому many.)

9. She has a lot of books.
   (Книги можно посчитать, но в утверждении чаще используется a lot of.)

2)

1. There weren't many animals.
   (Животных можно посчитать.)

2. Is there much snow?
   (Снег — неисчисляемое слово.)

3. I haven't got many shoes.
   (Обувь здесь имеется в виду как пары обуви, которые можно посчитать.)

4. It has many legs.
   (Ноги можно посчитать.)

5. They are much older than me.
   (Much используется перед сравнительной степенью: much older.)

6. Did you watch many movies?
   (Фильмы можно посчитать.)

7. Thank you very much.
   (Устойчивое выражение.)

8. I made a lot of mistakes.
   (Ошибки можно посчитать, но в утверждении часто используется a lot of.)

9. For how many nights?
   (Ночи можно посчитать.)

Итоговое правило:

• much — с неисчисляемыми словами: water, coffee, snow, noise, money. Обычно в вопросах и отрицаниях.

• many — с исчисляемыми словами во множественном числе: eggs, cars, books, animals.

• a lot of — подходит и для исчисляемых, и для неисчисляемых слов в утверждениях: a lot of books, a lot of water.