Infinitely many solutions
Explanation:The given system of equations is:
12x + 6y = 6..........(1)
4y = -8x + 4............(2)
Divide equation (1) by 6
[tex]\begin{gathered} \frac{12x}{6}+\frac{6y}{6}=\text{ }\frac{6}{6} \\ 2x\text{ + y = 1} \\ y\text{ = -2x +1}\ldots\ldots\ldots\ldots.(1) \end{gathered}[/tex]Divide equation (2) by 4
[tex]\begin{gathered} \frac{4y}{4}=\text{ }\frac{-8x}{4}+\frac{4}{4} \\ y\text{ = -2x + 1}\ldots\ldots\ldots(2) \end{gathered}[/tex]Equations (1) and (2) are equal, they have infinitely mny solutions
