Simplifying Rational Powers

Bah, okay. (Doh)

I'm trying to find a common denominator right now for this part of the problem:

$\displaystyle 4/3-5/6$

Don't I multiply the denominators together? Thus making it?

$\displaystyle 24/18-15/18$

Now since I can subtract the numerators it means I get 9. $\displaystyle 9/18 = 1/2$

That ends up as the right answer for the exponent of this: $\displaystyle 12x^1/2/y^4/3$

However, in the solution it baffles me because they got the following:

$\displaystyle = (4*3)x^4/3-5/6/y^4/3$

= 12x^8/6-5/6/y^4/3

It looks like they just multiplied it by two, but I didn't think that was how you got a common denominator...

$\displaystyle = 12x^1/2/y^4/3$