Find $x$ and $y$. \[ \left[\begin{array}{rr} 1 & 2 x \\ y & -6 \end{array}\right]=\left[\begin{array}{rr} 1 & -12 \\ -2 & -6 \end{array}\right] \]

Step 1 ：The given problem is a matrix equation. To solve for x and y, we need to equate the corresponding elements of the two matrices. This will give us two equations, which we can then solve to find the values of x and y.

Step 2 ：From the first column of the matrix, we get the equation \(y = -2\).

Step 3 ：From the second column of the matrix, we get the equation \(2x = -12\). Solving this equation gives us \(x = -6\).

Step 4 ：The solution to the system of equations is \(x = -6\) and \(y = -2\).

Step 5 ：Final Answer: \(\boxed{x = -6, y = -2}\)