We need to examine each expression at a time.
(A) x^2 + x - 6
notice the -6 has factors 3 and -2 which could be used to reverse the FOIL method:
x^2 + x - 6 = x^2 + 3 x - 2 x - 6 = x( x + 3) - 2 (x + 3) = (x+ 3) (x - 2)
(B) In this cubic expression we cannot use the reverse FOIL to extract factors.
(C) 4 x^2 - 2 x + 1 We cannot reverse the FOIL property either.
(D) x^2 + 8 x + 12
We notice that 12 has factors 2 and 6 which can be used to factor out this expression as shown below:
x^2 + 2 x + 6 x + 12 = x (x + 2) + 6 (x + 2) = (x + 2) (x + 6)
Therefore we were able to use the reverse of the FOIL property in expressions (A) and (D).