If in the 6 months he visits your site as a direct visit and buy than this conversion will be attributed to the previous campaign. A Direct visits never overrides a previous visit.
If he comes back to your website through a search engine, referral link, any other campaign or as a direct after more than 6 months after the last visit, and buy than that conversion will be attributed to this last origin.
Google Analytics has a last touch attribution model in the sense that the conversions are always attributed to the last traffic source that drove the visitor to your site.
You can always go into the Multi-channel Funnel reports to see which traffic sources didn't convert but assisted on conversions. An assisted conversion is a conversion that was not the last, but drove that visitor to the site at some point of his life.
By some point of his life I mean some point of the cookie life, since all this data is tied back together on GA backend through a random UserId that is stored on cookie __utma.
Users with access to Google Analytics Premium also have the option to use the "Attribute Modelling Tool". With this tool you can experiment different attribution models as First touch, Time decay, or even a custom model.