Write the equation of the line in slope-intercept form.

perpendicular to y = 2x+6 and

passing through (-4,2)

Equation of the perpendicular

y = 2x+6

slope of the perpendicular = 2

slope of the req. line = - 1/2

equation of the req. line

y - y1 = m (x - x1)

y - 2 = - 1/2 (x + 4)

2 (y - 2) = - 1 (x + 4)

2y - 4 = - x - 4

2y = - x

y = (-1/2) x

this is your req. equation of line.