Looks like you're given an equality between two matrices,
[tex]\begin{bmatrix}-12&-w^2\\2f&3\end{bmatrix}=\begin{bmatrix}2k&-81\\-14&3\end{bmatrix}[/tex]
Two matrices are equal if the entries in the same positions (row and column) are equal. This means
[tex]\begin{cases}-12=2k\\-w^2=-81\\2f=-14\\3=3\end{cases}[/tex]
We can ignore the last one, since it's clearly true. For the remaining, we get
[tex]-12=2k\implies k=-\dfrac{12}2=-6[/tex]
[tex]-w^2=-81\implies w^2=81\implies w=\pm9[/tex]
[tex]2f=-14\implies f=-\dfrac{14}2=-7[/tex]
