You can download a trial version of FMP 11 (30 day trial, from the downloads area of the FMP site: LINK) to convert your FMP 6 solution to fmp.7; then you would open the file in your final version (FMP 15?) to convert to fmp.12 file type. You will likely need to update scripts, as the conversion is likely to leave you with some broken functionality if you have a number of scripts in your solution. In my case, I've found that exporting the old data and importing into a new solution developed in the current version was easier than trouble shooting all the broken scripts and deprecated functionality. But I do that after converting so that I can see what breaks and what doesn't.
You may also have an old solution designed with several related files, while modern FMP options support multiple tables in a single file. Therefore, you may opt for a different design.
I also recommend using FileMaker Advanced. The database design report combined with such third party tools as Base Elements can be very useful in evaluating your converted files and locating any parts that may have issues.