Let's solve the equation $6 = 3 + 2(-x - 8)$:

1. First, distribute the $2$ to the terms inside the parentheses:

$6 = 3 + 2(-x) + 2(-8)$

$6 = 3 - 2x - 16$

2. Simplify the right-hand side:

$6 = -2x - 13$

3. Add 13 to both sides to isolate the $-2x$ term:

$6 + 13 = -2x$

$19 = -2x$

4. Finally, divide both sides by $-2$ to solve for $x$:

$x = \frac{19}{-2} = -\frac{19}{2}$

So, the solution is $x = -\frac{19}{2}$.

Would you like further details on any step?

Here are 5 related questions to deepen understanding:

1. How do you solve equations with multiple steps like this one?
2. What happens if we distribute incorrectly in such an equation?
3. How would you check if $x = -\frac{19}{2}$ is the correct solution?
4. How does adding or subtracting terms on both sides help in solving equations?
5. What if you had variables on both sides of the equation?

Tip: Always remember to simplify both sides of the equation as much as possible before solving!