How do you factor x^2+4x-12?

The answer is $\left(x - 2\right) \left(x + 6\right)$
Determine what two numbers when added together make the coefficient of $x$, in this case $4$, and when multiplied together make the constant, in this case $- 12$. For this problem, the two numbers are $6$ and $- 2$.
$6 + \left(- 2\right) = 4$, and $6 \times \left(- 2\right) = 12$.
The factorization of ${x}^{2} + 4 x - 12 = \left(x - 2\right) \left(x + 6\right)$.