Identify the greatest common factor (GCF) of all terms in the expression 2x2 - 8x - 12.

The terms are $2x^2$, $-8x$, and $-12$.
The numerical coefficients are 2, $-8$, and $-12$. The greatest common factor of these numbers is 2.
There is no common variable factor since the last term, $-12$, does not contain $x$.

We look for two numbers that multiply to $-6$ and add to $-4$.
The pairs of integer factors for $-6$ are $(1, -6)$, $(-1, 6)$, $(2, -3)$, and $(-2, 3)$.
Their sums are:
$1 + (-6) = -5$
$-1 + 6 = 5$
$2 + (-3) = -1$
$-2 + 3 = 1$
None of these sums equal $-4$. Therefore, $x^2 - 4x - 6$ cannot be factored further over integers.