To simplify the expression \( 4(2 - x) + 2x(2 - x) \), we will distribute the terms step by step.
First, distribute \( 4 \) in the first term: \[ 4(2 - x) = 4 \cdot 2 - 4 \cdot x = 8 - 4x \]
Next, distribute \( 2x \) in the second term: \[ 2x(2 - x) = 2x \cdot 2 - 2x \cdot x = 4x - 2x^2 \]
Now, we can combine the two results: \[ 8 - 4x + 4x - 2x^2 \]
The \(-4x\) and \(4x\) terms cancel each other out: \[ 8 - 2x^2 \]
Thus, the expression \( 4(2 - x) + 2x(2 - x) \) simplifies to: \[ \boxed{8 - 2x^2} \]