There are lots and lots of times when you will want to mix languages. It happens so often in some foci of coding that languages are built to integrate utilities not native to them (scripting languages do this a lot).
If a project is really big, often times you will mix languages. Need a lot of data manipulation? Write a script. Need to store the data somewhere? Use a query language. The program might be mainly coded in, say, c++ or Java, but you might still have to do other things that are simply much more efficient in some other language. The game League of Legends, for example, has about 7 or 8 different languages to run (I typed "ruin" here initially, which might also be accurate) its interfaces and control its gameplay.
For a lot of projects, you typically don't have to mix languages. Most high level languages can do everything you'd want them to do (need a GUI with C++? There's QT. GUI with Java? Try Swing).
Mixing languages can be problematic come debugging time, but that's typically only when you're mixing languages in cases where you simply do not need to do so. If you're learning how to code, I would highly recommend writing a bunch of different programs utilizing a CLI before you move on to trying to code GUIs. Once you can solve some complex problems (try to find a way to implement and use a red-black tree, for example), move on to working with GUIs. You often have to learn all the nuances of different GUI designer APIs, which will be a lot to focus on.
What exactly is the problem you're trying to solve? If you have AIM, leave your screen name and I could help you there (should this be something you intend to be proprietary).
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