There are a number of ways that would be useful.
1. more inputs. Hook the outputs of the mixer into 2 of the inputs on the powered mixer to gain channels while still using the powered mixers amps to drive the speakers.
2. monitoring. Use the mixer for the mains, hooked to a power amp then the main speakers. take an aux send from the mixer and run it into the powered mixer to run the monitors.
3. any other combination you could think of. there is no right way to do this, it sounds like someone creatively trying to put together what they have lying around to do what they need without having to buy the equipment to do it 'right'.