To solve the equation \(2(x+2) = 4^2\), we can start by simplifying the right-hand side.
First, calculate \(4^2\): \[ 4^2 = 16 \]
Now, the equation becomes: \[ 2(x+2) = 16 \]
Next, we can divide both sides of the equation by 2 to isolate \(x + 2\): \[ x + 2 = \frac{16}{2} \] \[ x + 2 = 8 \]
Now, subtract 2 from both sides to solve for \(x\): \[ x = 8 - 2 \] \[ x = 6 \]
Thus, the missing value is \(\boxed{6}\).