$$\begin{array}{rll}
(x+2)(x-2)&=&x(x-2)+2(x-2)\\
&=&x^2-2x+2x-4\\
&=&x^2-4
\end{array}$$
You really need to learn to recognise this as a difference of squares.
The brackets are the same except one has a - and the other has a +
$$\boxed{(x+a)(x-a)=x^2-a^2}$$
.