What is the slope of a line that is perpendicular to the line of 2x+4y=12

make the equation slope-intercept form:

subtract 2x from both sides:

4y = - 2x + 12

divide by 4 to get y by itself:

y = - 1/2x + 3

to make the new line perpendicular to the existing line, completely flip the slope of the line:

y = 2x + 3