I need help , I really don’t understand it .

Answer:
slope intercept form is the form of y=mx+b, where the slope is m and the y intercept is b.
what you have to do is to solve the equations for y.
1) 2x+2y = 10
2y = 10 -2x
y = -x +5
2) 12+4y = -4x
4y = -4x-12
y = -x -3
lines are parallel when they have same slope and different y-intercepts. m1=m2 and b1 ≠ b2
lines are perpendicular when the multiplication of their slope gives -1
m1 x m2 = -1
here the slopes are same and y-intercepts are different so lines are parallel.