Welcome to the community. Yes, you can upgrade to CS6 from your existing version which is CS3. Do you have the full version CS3 or upgraded to CS4 from an older version?
Thanks for your reply..I have the full version CS3!
Depending on the suite that you own, you can choose from the list of suites to which you want to upgrade, and buy the same from this URL: http://www.adobe.com/products/catalog/cs6._sl_id-contentfilter_sl_catalog_sl_software_sl_c reativesuite6.html
You cannot upgrade from CS3 to CS6. You will have to pay full price and you
will be getting an outdated suite of products. You will be far better off
moving to Creative Cloud. The first year will be $29.99/month. After that
the regular price is $49.99/month and includes everything in CS6 as well as
the new CC apps.