Since you can't subtract 6/12 from 3/12 rename 7 3/12 as 6 15/12. why?

Because 3 is not large enough to subtract 6 from. 
Let's look at it this way:
I like to think of mixed number as pizzas and pizza slices. in the mixed number 7&3/12, 7 represent 7 whole pizzas, the denominator 12 represents the number of slices each pizza can be cut into, and the numerator 3 represents three slices (in the 8th pizza). when you subtract 6/12 from 7 and 3/12, since 6 is the numerator which represents slices, you are trying to take away 6 slices. but you only have 3 slices, that is not enough, so you cut one of the whole pizzas into 12 slices, now you have 6 whole pizza left and 15 slices, now you can give away 6 slices from the 15 slices.
I hope this makes sense to you.
you use this method to do addition and subtraction. when you do mixed number multiplication and division, you have to cut all the wholes into slices. well, that's a topic for another day.