Hello, how long are the periods of the visa type "single" and "double" ?

If you only visit HK, you won't need one because you can stay in HK for 90 days at most without visa. Considering of your 4-6 weeks trip, I think a single entry one is OK as long as you don't exit during your stay. Don't worry if you just get a L type for 30 days duration. You can extend it at the entry and exit management bureau. No matter it is "single" or "double", the consular officers decide how long the periods are.