The function in the problem is given as:

$f(x) = 2|x - 8|$

You are asked to evaluate $f(x)$ for several values and expressions of $x$. Let’s go through each part.

1. $f(-2)$: $f(-2) = 2|-2 - 8| = 2|-10| = 2 \times 10 = 20$

2. $f(0)$: $f(0) = 2|0 - 8| = 2|-8| = 2 \times 8 = 16$

3. $f(2)$: $f(2) = 2|2 - 8| = 2|-6| = 2 \times 6 = 12$

4. $f(x+1)$: $f(x+1) = 2|x+1 - 8| = 2|x - 7|$

5. $f(x^2 + 2)$: $f(x^2 + 2) = 2|x^2 + 2 - 8| = 2|x^2 - 6|$

Here are the calculated answers for each part:

1. $f(-2) = 20$
2. $f(0) = 16$
3. $f(2) = 12$
4. $f(x+1) = 2|x - 7|$
5. $f(x^2 + 2) = 2|x^2 - 6|$

Would you like further details on any of these steps, or do you have any questions?

Here are some related questions for further practice:

1. How would you evaluate $f(x)$ if the function involved a different absolute value transformation, like $f(x) = 3|x - 5|$?
2. Can you calculate $f(x - 3)$ for the given function $f(x) = 2|x - 8|$?
3. How does the absolute value affect the symmetry of the function $f(x) = 2|x - 8|$?
4. What is the domain and range of $f(x) = 2|x - 8|$?
5. How would you find the x-intercepts of $f(x) = 2|x - 8|$ if it crosses the x-axis?

Tip: Always simplify inside the absolute value before applying any transformations or multipliers outside.