Answer
Infinite solutions
Work Step by Step
Please see the screenshot of the tables for the two equations.
Purple line: $x-2y=-6$
Green line: $-2x+4y=12$
Purple line:
$x-2y=-6$
$x-2y+2y+6=-6+2y+6$
$x+6=2y$
$(x+6)/2=2y/2$
$1/2*x+3=y$ ($m=1/2$, y-intercept is 3)
Green line:
$-2x+4y=12$
$-2x+4y+2x=12+2x$
$4y=2x+12$
$4y/4=(2x+12)/4$
$1/2*x+3=y$ ($m=1/2$, y-intercept is 3)
The two lines have the same slope and y-intercept. Thus, the two lines are actually the same line and have an infinite number of solutions.