Let's analyze the given matrix equation from the image:

We have three matrices $A$, $B$, and $C$:

$A = \begin{bmatrix} 2x & 3 \\ -2 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 5 \\ 2 & x \end{bmatrix}, \quad C = \begin{bmatrix} 2y & 26 \\ -2y & -6 \end{bmatrix}$

The equation $A \cdot B = C$ implies matrix multiplication between $A$ and $B$, and their product should equal matrix $C$. We are tasked with finding the value of $2x^2 - y$.

Step 1: Perform matrix multiplication $A \cdot B$

To multiply matrices $A$ and $B$, we'll follow the rule of matrix multiplication: the entry in the $(i,j)$-th position of the product is obtained by taking the dot product of the $i$-th row of matrix $A$ with the $j$-th column of matrix $B$.