I have a Azden fmx-22 mixer that I will connect a NTG-2 to and from there it will go into a Panasonic HDC Z10000 camera.
How do I set the levels of the camera to the mixer if the mixer doesn't have a reference tone generator?
If you have enough time in advance you could pick up a cable tester that has a tone generator in it for about $20. Here's one. Pull it into the studio, run it through your mixer, and mark the point at which its output = -20 dbfs. It'll probably be close to unity gain. Then when you're out in the field you can just plug the tester into the mixer, set the gain to the same spot, and calibrate your camera input.
an alternative to this method would be to render a sine wave at -20 dbfs in your DAW and put that file on your phone. Turn your phone's volume all the way up, plug it into your mixer (you'll probably need a 35mm to xlr adapter) and repeat the same steps as above.
Grant's solution works, but what I often do if the mixer has a limiter, is to simply crank up the gain, do some noise that makes the signal bounce against the limiter (which is then the mixers highest output) and then adjust the cam so that signal is just below 0. Now, everything should hit the limiter before they can distort the cam.