Let's solve the inequality step-by-step:

The given inequality is: $-5(x - 4) \geq 2(1 - x)$

1. First, distribute both sides: $-5x + 20 \geq 2 - 2x$

2. Now, collect all $x$-terms on one side and constants on the other side: $-5x + 2x \geq 2 - 20$ Simplifying both sides: $-3x \geq -18$

3. Divide both sides by -3. Remember, when dividing by a negative number, the inequality flips: $x \leq 6$

Thus, the solution is $x \leq 6$.

The correct answer is C. $x \leq 6$.

Would you like more details on this solution or have any questions?

Here are some related questions:

1. What happens if you divide by a negative number in an inequality?
2. How do you solve inequalities involving fractions?
3. What is the difference between solving an equation and solving an inequality?
4. Can you graph the solution $x \leq 6$ on a number line?
5. How would you solve a compound inequality like $2 \leq x + 3 \leq 8$?

Tip: When solving inequalities, always watch for when you multiply or divide by negative numbers, as this will flip the inequality sign.