Say you have the term: $-3x^2+12$ and you want to factor it out:
$$-3(x^2 - 4)$$ $$-3((x+2)(x-2))$$
However you can also write the above as:
$$-3(x+2) (x-2)$$
But in many other cases, e.g if you have $3(4 + 5)$, you can't just turn that into $3(4) + 5$ as you'll get a different result. What's the intuition behind being able to do that in the above example?
You can do the above example because $(x+2)$ and $(x-2)$ are multiplied together. If you add them together, notice that $$-3((x+2)+(x-2))\neq-3(x+2)+(x-2)$$ The general rule is that $$a(bc)=abc$$ $$a(b+c)=ab+ac$$