Manipulating Categories on the main page

I would like to exclude subcategories from the main page but when you click on a specific category, on that page, I would like to have all the child categories listed.

For example, say you have category called “cars” and under that category, you have “blue cars” and “red cars”.

On the main page, it will only show cars with post count. When a user clicks on the cars, it should list the child categories “Blue Cars” and “Red Cars” underneath the Main Category “Cars”.

How should I go about doing this?