Let's expand both expressions using the formula (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3:

(x+2)^3 = x^3 + 6x^2 + 12x + 8
(x-2)^3 = x^3 - 6x^2 + 12x - 8

Now, subtract the second expression from the first:

(x+2)^3 - (x-2)^3 = (x^3 + 6x^2 + 12x + 8) - (x^3 - 6x^2 + 12x - 8)
(x+2)^3 - (x-2)^3 = x^3 + 6x^2 + 12x + 8 - x^3 + 6x^2 - 12x + 8
(x+2)^3 - (x-2)^3 = 12x^2 + 24

Now, set this equal to 64 and solve for x:

12x^2 + 24 = 64
12x^2 = 40
x^2 = 40/12
x^2 = 10/3
x = +/- sqrt(10/3)

Therefore, x = +sqrt(10/3) or x = -sqrt(10/3).