You said . . . -12√12 - 2√3 .
Before we get all tangled up trying to work on the whole thing at once,
take a look at that first square root: √12 .
That's the same thing as √(4 · 3) and you can break it up like this:
√(4 · 3) = √4 · √3 .
Now, we know what √4 is . . . it's just 2 .
So we can write the first half of your original big quantity like this:
-12 √12
= -12 · 2 · √3
= -24√3 .
NOW, finally, let's go back and rewrite the whole thing:
-24√3 - 2√3 .
Isn't that a lot nicer looking ?
It's nearly solved all by itself ... if you don't let the √3 scare you.
It just says -24(cows) - 2(cows) .
and everybody knows, that's just -26(cows).
So -24√3 - 2√3 is just -26√3 . (choice-C)