given, ∣x^2 − x − 6∣ = x + 2

Or I (x-3)*(x+2)I = (x+2)

Case 1) When x > 3

Then (x-3)*(x+2)= (x+2) or x -3 =1 or x = 4

Case 2) when – 2 <= x < 3, -(x-3)*(x+2)= (x+2)

-(x-3)*(x+2) – (x+2) =0

(x+2)(x-3+1) =0

(x-2)*(x+2) =0

x = 2 or -2

case 3 ) when x < – 2

(x-3)*(x+2) = (x+2)

x = 4 (not possible as x < -2

so required product = 4*2*(-2) = -16