Hi Amy!
Sorry I didn't explain more clearly before...
I'm assuming you mean thirds, sixths, and tenths apart with hands together in similar motion. If that is the case, then you would play C major third apart like this:
Right Hand: E F G A B C D E (A third above the Left Hand)
Left Hand : C D E F G A B C (regular C major scale)
So basically your left hand is playing the C major scale while your right hand is playing a scale a major third above.
Hope that helps...for a sixth apart, your hands would be going (in C major):
Right Hand: C D E F G A B C (regular C major scale)
Left Hand : E F G A B C D E (a sixth below Right Hand)
Its just the same as the 3rd apart, except your right hand has the C major scale now while your left hand is playing a sixth below it.
I've never played tenths, but I assume it would be the same except your hands are a tenth apart. You should probably ask your teacher since I'm assuming all this for hands together, a 3rd/6th apart, and in similar motion.