evaluate each limit, if it exists

[(2+x)^2 - 16]/ (x-2)

what do I do?

At what value of x do you want the limit? Is it at x = 2, where the denominator vanishes?

The numerator is the difference of two squares, andcan be written
(2 + x -4)(2 + x +4)= (x-2)(x+6)

Cancel out the x-2 therms in numerator and denominator anbd you are left with
x + 6. You can easily evaluate that at any value of x, including x=2