I am have four different document libraries and each document library has two folders. I want to show my folders under document library in quick launch in SharePoint. I tried to modify from navigation settings but I haven't found anything helpful.
The navigation settings (even in Publishing sites) do not allow for dynamic content to be added as such. You would either have to modify the master page (preferably your own copy, not the default one) and include a web part zone under the .ms-quicklaunch CSS. Than you envision using DVWP or XLVT.
Of course, there are alternatives, but more complex, e.g. use Delegate controls,
From the way you describe it the solution does not need to be dynamic? In this case you can simply add your own links in the Navigation settings.
First create a Heading which links to your library then create links which go directly to your folders and position them under the library heading. If you are not sure how to get these URLs then go to your library and click on the folder then copy the URL from the browser.