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We are asked to solve the matrix equation:

\[
-3A + 6B
\]

where the matrices \( A \) and \( B \) are given as:

\[
A = \begin{bmatrix} -4 & -5 & 2 \\ -5 & -3 & 5 \end{bmatrix}
\]

and

\[
B = \begin{bmatrix} 6 & 1 & -1 \\ -7 & 8 & -9 \end{bmatrix}.
\]

Let's break it down step by step.

### Step 1: Calculate \(-3A\)
Multiply each element of matrix \( A \) by \(-3\):

\[
-3A = -3 \times \begin{bmatrix} -4 & -5 & 2 \\ -5 & -3 & 5 \end{bmatrix}
= \begin{bmatrix} 12 & 15 & -6 \\ 15 & 9 & -15 \end{bmatrix}.
\]

### Step 2: Calculate \(6B\)
Now, multiply each element of matrix \( B \) by \(6\):

\[
6B = 6 \times \begin{bmatrix} 6 & 1 & -1 \\ -7 & 8 & -9 \end{bmatrix}
= \begin{bmatrix} 36 & 6 & -6 \\ -42 & 48 & -54 \end{bmatrix}.
\]

### Step 3: Add \(-3A\) and \(6B\)
Now, add the two matrices:

\[
-3A + 6B = \begin{bmatrix} 12 & 15 & -6 \\ 15 & 9 & -15 \end{bmatrix} + \begin{bmatrix} 36 & 6 & -6 \\ -42 & 48 & -54 \end{bmatrix}
= \begin{bmatrix} 48 & 21 & -12 \\ -27 & 57 & -69 \end{bmatrix}.
\]

Thus, the result of \(-3A + 6B\) is:

\[
\begin{bmatrix} 48 & 21 & -12 \\ -27 & 57 & -69 \end{bmatrix}.
\]

### Conclusion:
The correct answer matches option **d**.

Would you like more details or have any questions?

Here are five related questions to expand this problem:
1. How do we handle matrix multiplication with different dimensions?
2. What happens if you multiply matrices \(A\) and \(B\) instead of scalar multiplication?
3. How can you solve for \(A\) or \(B\) if you're given a similar equation?
4. How do scalar and matrix operations differ from one another?
5. What is the effect of changing the scalar on the operation \( -3A + 6B \)?

**Tip:** When performing matrix operations, always ensure the dimensions of the matrices are compatible for addition, subtraction, or multiplication!

Find -3A + 6B where A = [[-4, -5, 2], [-5, -3, 5]] and B = [[6, 1, -1], [-7, 8, -9]].

Learn how to solve the matrix equation -3A + 6B using given matrices A and B with a detailed step-by-step solution. This problem involves matrix operations such as scalar multiplication and addition, suitable for students in Grades 10-12.

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