Taxonomy and menu links I have an example content type "Cars" and two vocabularies: "Country" with some terms of countries and "Brand" with some terms of brands.

The content type will have three more field that will be term references: Country, Brand and Type of cars.

I'm using a view page with path /cars that displays all the contents from that content type. The "Country" and "Brand" I'm using them as a exposed filters.

So my goal is to create a menu links from the left sidebar with type of cars like Hatchbacks, sports cars, city cars... etc. and will display the number how many cars are hatchbacks, how many sports cars....

When a user click on some of the menu links from left like for an example "Hatchbacks" it will display all the hatchbacks. And after that the filters Country and Brand will stay so a user can filter them.

My question is how can I create such menu links and will display the numbers of the nodes?

I'm using Drupal 7.
I used the taxonomy menu module on my latest project for this purpose, works like a champ!
Here is a quote about it (from the module's project page):

Transforms your taxonomy vocabularies into menus with ease!
Features:

Custom Menu per vocabulary
Uses the default taxonomy term path or custom paths
Integrate with Views
Integrate with Pathauto: use URL/path aliases
Does not interfere with other menu modules