1. **State the problem:** Simplify the expression $\left(x-2\right)^2 + 16\left(2-x\right)$.\n\n2. **Recall formulas and rules:** The square of a binomial is given by $\left(a-b\right)^2 = a^2 - 2ab + b^2$. Also, note that $2-x = -(x-2)$, which will help simplify the second term.\n\n3. **Expand the square:**\n$$\left(x-2\right)^2 = x^2 - 2 \cdot x \cdot 2 + 2^2 = x^2 - 4x + 4$$\n\n4. **Rewrite the second term using the negative sign:**\n$$16\left(2-x\right) = 16\left(-\left(x-2\right)\right) = -16\left(x-2\right)$$\n\n5. **Substitute back and combine:**\n$$x^2 - 4x + 4 - 16\left(x-2\right)$$\n\n6. **Distribute the $-16$:**\n$$x^2 - 4x + 4 - 16x + 32$$\n\n7. **Combine like terms:**\n$$x^2 - 4x - 16x + 4 + 32 = x^2 - 20x + 36$$\n\n**Final answer:**\n$$x^2 - 20x + 36$$