It seems the relation you provided has been repeated, and we need to clarify a bit. It looks like the original relation is:

$-3x^2 - 6x = -3x + 2y$

Step 1: Solve for $y$ in terms of $x$

1. Start by simplifying and isolating $y$: $-3x^2 - 6x = -3x + 2y$

2. Add $3x$ to both sides to remove it from the right: $-3x^2 - 3x = 2y$

3. Now, divide both sides by $2$ to isolate $y$: $y = \frac{-3x^2 - 3x}{2}$ $y = -\frac{3}{2}x^2 - \frac{3}{2}x$

Step 2: Substitute $x = -2$ and evaluate $y$

Now that we have $y$ as a function of $x$: $y = -\frac{3}{2}x^2 - \frac{3}{2}x$

Substitute $x = -2$: $y = -\frac{3}{2}(-2)^2 - \frac{3}{2}(-2)$

Calculate each term:

1. $(-2)^2 = 4$
2. $-\frac{3}{2} \cdot 4 = -6$
3. $-\frac{3}{2} \cdot (-2) = 3$

So, $y = -6 + 3 = -3$

Final Answer

When $x = -2$, $y = -3$.

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Would you like further details or have any other questions?

Here are some related questions that might help you understand this process further:

1. How do we handle exponents when substituting values?
2. What are the steps for isolating a variable in an equation?
3. Why do we simplify terms before substituting a value?
4. How does dividing both sides of an equation affect each term?
5. Why is it important to evaluate each step individually when substituting?

Tip: Always simplify the equation fully before substituting values to minimize errors in calculation.