Dekimasuka or dekimasenka

I am studying Japanese with Rosetta Stone, and sometimes the correct answer is to ask "dekimasuka" and other times, "dekimasenka." The program doesn't explain when each one should be used; you're supposed to figure it out by looking at the accompanying picture, but I don't get it. I can find anything on google either, so I would appreciate it if someone could help me out here. Thanks.

It's not so different from negative questions in English. What is the difference between "Will you play golf?" and "Won't you play golf?"

I don't know the situations, so I can't clarify more, but the negative is often a supposing nuance, and often an invitation. But it's case by case.

I agree with nahadef.

Also, I noticed that dekimasenka would be mostly used when you ask permission for yourself. And dekimasuka usually when you ask someone if there's a possibility for them to do a certain task. This observation though is not 100% done all the time and either can be interchangeable in the same situations.

It's a confusing thing, really, but not at all destructive... just a couple of practices and you should be able to get the hang of it.