For what value of x is the double product of the binomials x+2 and x–2 is 16 less than the sum of their squares?

(x + 2)(x - 2) = (x+2)^2 + (x - 2)^2 -16
x^2 - 4 = 2x^2  + 4x - 4x + 8 - 16
x^2 - 4 =  2x^2  - 8
x^2  = 4 
x  =  +/- 2

x = -2 is the only value which fits the original equation  so that's the answer.