Hello!
First, we have to solve this system, then we can classify it.
Let's solve:
[tex]\begin{cases}4x+2y=-6 \\ 2x+y=8\end{cases}[/tex]Let's isolate y in the second equation:
[tex]y=8-2x[/tex]Now, let's replace it in the first equation:
[tex]\begin{gathered} 4x+2y=-6 \\ 4x+2\cdot(8-2x)=-6 \\ 4x+16-4x=-6 \\ \cancel{4x}+16\cancel{-4x}=-6 \\ 16=-6 \\ \text{FALSE!!!} \end{gathered}[/tex]As we can see, this linear system has no solution.
Now, let's classify it:
As this does not admit any solution, we can say that it is inconsistent.