Why is the result of $-2^2 = -4$ but $(-2)^2 =4$? I am really new into math, why is $-2^2 = -4 $ and $(-2)^2 = 4 $? 

It is true that $-2^2$ is ambiguous (unless you know the convention), because $-(2^2) \ne (-2)^2$.  (And, indeed, some calculators or programing languages may do it using their own convention, different from the mathematicians' convention.) The mathematicians' convention is $-2^2 = -(2^2)$.  Why?  Presumably because we often need to write $-(2^2)$.  But if you ever need to write $(-2)^2$ you can just write $2^2$ instead.
