If two matrices are equal, then each of its elements must be equal.
If:
[tex]\begin{bmatrix}{a+3} & {4} \\ {6} & {b-1}\end{bmatrix}=\begin{bmatrix}{-3} & {4} \\ {6} & {2}\end{bmatrix}[/tex]This means that:
[tex]\begin{gathered} a+3=-3 \\ 4=4 \\ 6=6 \\ b-1=2 \end{gathered}[/tex]Isolate a and b from their respective equations to find their value:
[tex]\begin{gathered} a+3=-3 \\ \Rightarrow a=-3-3 \\ \therefore a=-6 \end{gathered}[/tex][tex]\begin{gathered} b-1=2 \\ \Rightarrow b=2+1 \\ \therefore b=3 \end{gathered}[/tex]Therefore, the value of a is -6 and the value of b is 3.