Solution:

As, $\left[ \begin{matrix} a+3 & 4 \\ 6 & b-1 \\ \end{matrix} \right]=\left[ \begin{matrix} -3 & 4 \\ 6 & 2 \\ \end{matrix} \right]$

By comparing the corresponding elements, we get

$a+3=-3$

$a=-3-3$

$a=-6$        

and               

$b-1=2$

$b=2+1$

$b=3$         

Hence

$a=-6$ and $b=3$