Think of two numbers that multiply to give 6 and add or take-away to give 1. Hmmm... Well 3 and 2 will work because their difference is 1 and 3 x 2 = 6 so now we need to think about the signs. We have
x²-x-6 = (x _ 3)(x _ 2).
When we times them together we get -6. To get a minus, one needs to be a + and the other needs to be a -. We need to get them to add to -1 so we can choose
I) 3-2 = 1 (nope)
II) 2-3 = -1 (yeah)
so it must be -3 and +2. This gives x²-x-6 = (x - 3)(x + 2).