We can solve the system of equations to check the number of system of the solutions.
y=-6x+2 ...(1)
-12x-2y=-4 ...(2)
Substitute -6x+2 for y in equation (2). So,
-12x-2(-6x+2)=-4
-12x+12x-4=-4 (By distribution property).
-4=-4 (-12x and +12x has been cancel out).
Notice x has vanish from the above equation and we are left with -4=-4 which is correct.
So, the system has infinte number of solutions.