1. **State the problem:** We are given two matrices $$A = \begin{bmatrix} 2 & -3 \\ -1 & 4 \\ 4 & 2 \\ 4 & 2 \end{bmatrix}$$ and $$B = \begin{bmatrix} -5 & -2 \\ 1 & -5 \\ 6 & -8 \\ 6 & 4 \end{bmatrix}$$ We need to find the matrix expression $$6A - 3B$$. 2. **Multiply matrix A by 6:** Multiply each element of matrix A by 6: $$6A = 6 \times \begin{bmatrix} 2 & -3 \\ -1 & 4 \\ 4 & 2 \\ 4 & 2 \end{bmatrix} = \begin{bmatrix} 12 & -18 \\ -6 & 24 \\ 24 & 12 \\ 24 & 12 \end{bmatrix}$$ 3. **Multiply matrix B by 3:** Multiply each element of matrix B by 3: $$3B = 3 \times \begin{bmatrix} -5 & -2 \\ 1 & -5 \\ 6 & -8 \\ 6 & 4 \end{bmatrix} = \begin{bmatrix} -15 & -6 \\ 3 & -15 \\ 18 & -24 \\ 18 & 12 \end{bmatrix}$$ 4. **Subtract 3B from 6A:** Subtract corresponding elements of matrices: $$6A - 3B = \begin{bmatrix} 12 & -18 \\ -6 & 24 \\ 24 & 12 \\ 24 & 12 \end{bmatrix} - \begin{bmatrix} -15 & -6 \\ 3 & -15 \\ 18 & -24 \\ 18 & 12 \end{bmatrix} = \begin{bmatrix} 12 - (-15) & -18 - (-6) \\ -6 - 3 & 24 - (-15) \\ 24 - 18 & 12 - (-24) \\ 24 - 18 & 12 - 12 \end{bmatrix} = \begin{bmatrix} 27 & -12 \\ -9 & 39 \\ 6 & 36 \\ 6 & 0 \end{bmatrix}$$ **Final answer:** $$6A - 3B = \begin{bmatrix} 27 & -12 \\ -9 & 39 \\ 6 & 36 \\ 6 & 0 \end{bmatrix}$$