$4: 2(3+1)=?$

Step 1 ：The question is asking for the result of the mathematical expression \(4: 2(3+1)\).

Step 2 ：The first step is to solve the operation inside the parentheses, which is \(3+1\).

Step 3 ：Then, we multiply the result by 2.

Step 4 ：Finally, we divide 4 by the result of the multiplication.

Step 5 ：The result of the mathematical expression \(4: 2(3+1)\) is \(\boxed{0.5}\).