Update : I looked at it a little closer:
x-2 = 3 (sqrt(x+2)) square both sides
x^2 - 4x + 4 = 9 (x+2)
x^2 -13x -14 = 0
Quadratic equation shows x = -1 and 14
14 - 3 sqrt (14+2) = 2
14 - 3 (sqrt16) = 2 ( look at your step where you get 11 sqrt (16) <---- this is where you made your error)
14 - 12 = 2 so 14 IS an answer only -1 is NOT.