Let's simplify the given expression step by step:

$-6y - 2(8y - 2)$

Step 1: Distribute the $-2$ to the terms inside the parentheses.

$-6y - 2(8y - 2) = -6y - (2 \times 8y) + (2 \times 2)$

$= -6y - 16y + 4$

Step 2: Combine like terms.

The like terms are $-6y$ and $-16y$.

$-6y - 16y = -22y$

So, the simplified expression is:

$-22y + 4$

Let me know if you want more details or have any questions! Here are 5 related questions to explore:

1. How would you solve the equation if $-6y - 2(8y - 2)$ was equal to 0?
2. What happens if the constants change in the original equation? For example, instead of $-6y$, what if it was $-3y$?
3. Can you explain how to distribute when there are three terms inside the parentheses?
4. How do you factor a similar expression like $-22y + 4$?
5. What is the effect of changing the sign of the terms inside the parentheses?

Tip: Always distribute negative signs carefully to avoid common sign errors.