what is x in the equation x^2-4x-12?

If you mean

x²-4x-12=0
(x-6)(x+2) = 0
x = {-2,6}

x² - 4x - 12 = 0
x² - 2x = 12 + 2²
x² - 2x = 12 + 4
(x - 2)² = 16
x - 2 = +/- 4

x = 4 + 2, x = 6
x = - 4 + 2, x = - 2

Answer: x = 6, - 2

Proof (x = 6):
6² - 4(6) = 12
36 - 24 = 12
12 = 12

Proof (x = - 2):
(- 2)² - 4(- 2) = 12
4 + 8 = 12
12 = 12

(x - 6)(x + 2)
unless you set this equal to zero this is as far as you can go...so
x^2 - 4x - 12 = 0
(x - 6)(x + 2) = 0
x = 6, -2
but the way you have it written it cannot be solved.

x^2 - 4x - 12
= x^2 + 2x - 6x - 12
= (x^2 + 2x) - (6x + 12)
= x(x + 2) - 6(x + 2)
= (x + 2)(x - 6)

x^2-4x-12=0
x^2-6x+2x-12=0
x(x-6)+2(x-6)=0
(x+2) (x-6)=0
x+2=0 or x-6=0
x= -2 or x=6

Following the order of operations, if x = 6:

6^2 - 4(6) - 12 =
36 - 24 -12 =
12 - 12=
0

If x = -2

2^-2 - 4(-2) -12 =
4 - (-8) - 12 =
12 - 12 =
0

x^2-4x-12 = x^2-6x+2x-12 = (x-6)(x+2)
here, x is a variable
& if x^2-4x-12 = 0, then x=-2 or 6

(x-6)*(x+2)= x^2-4x-12 so x can be 6 or -2