I was granted a Schengen visa type C with 6 days duration of stay, can I stay longer than that? And if I can what should I do?
No you are not allowed to do this unless you secure, either:
- An extension of your current visa
- Another Schengen visa
- A long-stay visa
- A residence card or permit from a Schengen country (or at least apply or, in some cases, qualify for one)
- Another citizenship
None of this can be done quickly and easily from within the Schengen area, the most likely option being the extension but even those are only supposed to be granted in exceptional cases, see e.g. Is it possible to extend a tourist Schengen visa (12 more days)?