$\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] X=\left[\begin{array}{cc}-6 & 10 \\ 4 & 9\end{array}\right]$. Then $X=$

Step 1 ：Find the inverse of the given matrix: $\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$. The inverse of a 2x2 matrix $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ is $\frac{1}{ad-bc}\left[\begin{array}{ll}d & -b \\ -c & a\end{array}\right]$. In this case, the inverse is $\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$.

Step 2 ：Multiply the inverse of the given matrix with the right-hand side matrix: $\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\left[\begin{array}{ll}-6 & 10 \\ 4 & 9\end{array}\right]$.

Step 3 ：Calculate the product: $\left[\begin{array}{ll}4 & 9 \\ -6 & 10\end{array}\right]$.

Step 4 ：\(\boxed{\left[\begin{array}{ll}4 & 9 \\ -6 & 10\end{array}\right]}\)