The given matrix equation is,
[tex] 1.5\left[\begin{array}{cc}x&6\\8&4\end{array}\right] +y\left[\begin{array}{cc}1&4\\3&2\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] [/tex].
Multiplying the matrices with the scalars, the given equation becomes,
[tex] \left[\begin{array}{cc}1.5x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\
[/tex]
Adding the matrices,
[tex] \left[\begin{array}{cc}1.5x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\ [/tex]
Matrix equality gives,
[tex] 1.5x+y=z\\
9+4y=z\\
12+3y=6z\\
6+2y=2 [/tex]
Solving the equations together,
[tex] y=-2\\
3y-1.5x=9\\
-1.5x=9+6\\
x=-10
[/tex]
We can see that the equations are not consistent.
There is no solution.
