First off, "answer to this matrix" doesn't make any sense. A matrix isn't a problem, it's an object, like a number or expression.
You're asked to compute the difference between two matrices. When you're given two matrices of same dimension (same number of rows and columns), the sum/difference of them is the matrix whose components are sums/differences of the corresponding components.
As a simple example,
[tex]\begin{bmatrix}1&0\\0&1\end{bmatrix}+\begin{bmatrix}1&2\\2&1\end{bmatrix}=\begin{bmatrix}1+1&0+2\\0+2&1+1\end{bmatrix}=\begin{bmatrix}2&2\\2&2\end{bmatrix}[/tex]
In this case,
[tex]\begin{bmatrix}-4&-5&5\\1&6&3\\-2&2&1\end{bmatrix}-\begin{bmatrix}-6&-1&-6\\6&-3&-2\\4&-1&-3\end{bmatrix}=\begin{bmatrix}-4-(-6)&-5-(-1)&5-(-6)\\1-6&6-(-3)&3-(-2)\\-2-4&2-(-1)&1-(-3)\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}-2&-4&11\\-5&9&5\\-6&3&4\end{bmatrix}[/tex]
