Solution:

$3\left[\begin{array}{ll}x & y \\ z & w\end{array}\right]=\left[\begin{array}{rc}x & 6 \\ -1 & 2 w\end{array}\right]+\left[\begin{array}{cc}4 & x+y \\ z+w & 3\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}3 x & 3 y \\ 3 z & 3 w\end{array}\right]=\left[\begin{array}{lc}x+4 & 6+x+y \\ -1+z+w & 2 w+3\end{array}\right]$

Comparing the corresponding elements of these two matrices, we get:

$3 x=x+4$

$\Rightarrow 2 x=4$

 

$\Rightarrow x=2$

 

$3 y=6+x+y$

$\Rightarrow 2 y=6+x=6+2=8$

 

$\Rightarrow y=4$

 

$3 w=2 w+3$

 

$\Rightarrow w=3$

 

$3 z=-1+z+w$

$\Rightarrow 2 z=-1+w=-1+3=2$

 

$\Rightarrow z=1$

 

$\therefore x=2, y=4, z=1$, and $w=3$