Looks like these are equal matrices,
[tex]\begin{bmatrix}x+4&t-5\\t+4&x-4\end{bmatrix}=\begin{bmatrix}y+3&z-1\\y+5&-2\end{bmatrix}[/tex]
Two (identically-sized) matrices are equal to each other if their entries in the same positions are equal. This means
[tex]\begin{cases}x+4=y+3\\t-5=z-1\\t+4=y+5\\x-4=-2\end{cases}[/tex]
From the last equation we get [tex]x=2[/tex]. Then
[tex]x+4=6=y+3\implies y=3[/tex]
[tex]t+4=y+5=8\implies t=4[/tex]
[tex]t-5=-1=z-1\implies z=0[/tex]
