From the image, we can observe that this problem involves row-reducing a matrix using elementary row operations to achieve reduced row-echelon form. To find the missing entry, let's analyze the given operations:

1. Current Matrix at R3 - R1 operation:

   From the initial matrix, $R_3 = R_3 - R_1$:

   1 & 2 & 0 & 6 \\ 0 & 1 & 3 & -5 \\ 1 & -2 & 4 & -2 \end{bmatrix}$$ Subtracting $$R_1$$ from $$R_3$$: \[ \text{New } R_3 = [1, -2, 4, -2] - [1, 2, 0, 6] = [0, -4, 4, -8]. \] So, the updated matrix is: $$\begin{bmatrix} 1 & 2 & 0 & 6 \\ 0 & 1 & 3 & -5 \\ 0 & -4 & 4 & -8 \end{bmatrix}$$

2. Following row operation: $R_1 + \frac{1}{2}R_3$: [ R_1 = [1, 2, 0, 6] + \frac{1}{2}[0, -4, 4, -8] = [1, 0, 2, 2]. ]

3. Following row operation: $R_3 + 4R_2$: [ R_3 = [0, -4, 4, -8] + 4[0, 1, 3, -5] = [0, 0, 16, -28]. ]

4. Dividing $R_3$ by $1/11$: [ R_3 = \frac{1}{11}[0, 0, 16, -28] = [0, 0, 1, -2]. ]

Now, at the final step, if the operations were done correctly, we arrive at the missing value needed in the reduced matrix. Let me know if you would like to confirm calculations further or need help understanding this.