Here are my attempts at solving 8 over 12
Fundamentally, it's a topology problem but the red discs are placed randomly and so you will need some creative thinking and experimentation. There are also two other games, by the same person, in the same vein, but are possibly easier if you find this one too difficult: 6 over 8 and 5 over 6.
Each game is in the Nokia Store for £1.00 - highly recommended for puzzle fans. I expect the first level you play in each of these will keep you busy for quite some time. Once you figure out the pattern in the first level, you might whizz through other levels, unless you win by luck ;-)