Put it into any calculator the way it is presented here, and it'll give the answer of 16.
The rules to do this are called Order of Operations. The following take precedence in the order they are given:
1. Parentheses
2. Exponents (i.e. powers and roots)
3. Multiply and Divide (equal precedence, apply as they occur from left to right)
4. Addition and Subtraction (equal precedence, apply as they occur from left to right.
The anagram PEMDAS is often used to remember these rules.
So for 8/2(2+2)
You must do (2+2) first.
Now it becomes 8/2(4), which is the same as 8/2x4
All that remains now is multiplication and division, which have equal precedence and you apply left to right as they occur:
So 8/2 is 4.
Thus 8/2x4 becomes 4x4, which is then 16.
Note that 8/2x4 is NOT 8/8. That only happens if you have 8/(2x4). Without the parentheses, you must do 8/2 first, which is 4, and then multiply 4 by 4.
A nice detailed explanation, and I believe the correct one. 16.