Answer
$\lambda=-3$
Work Step by Step
If A is an nxn matrix, a scalar $\lambda$ is called an eigenvalue of A is there is a non-zero vector $v$ such that $Ax=\lambda x$. This vector is called the eigenvector of A corresponding to $\lambda$.
Hence here, we compute:
$Av=\begin{bmatrix}
-1 &1 \\
6 & 0
\end{bmatrix}\cdot\begin{bmatrix}
1 \\
-2
\end{bmatrix}=\begin{bmatrix}
-3\\
6
\end{bmatrix}=-3\begin{bmatrix}
1 \\
-2
\end{bmatrix}=-3v$
Thus we can see that $\lambda=-3$