Any line parallel to the given line 


    4y + 8x = 28    (1)


has an equation


    4y + 8x = c     (2)


with the same left side as the given line (1) has  and some constant term "c" in the right side.


The constant term value "c" in (2) is determined from the condition that the point (-6,-3) lies on this line (2).


For it, substitute the coordinates  x= -6, y= -3 into equation (2) and determine "c".


    4*(-3) + 8*(-6) = c

    -12     - 48    = c

    -60             = c.


Thus you just determined  c = -60, and your equation is


    4y + 8x = -60.


You can simplify it by dividing both sides by 4


    y + 2x = - 15,


or, to get the requested form,


    y = -2x - 15.


It is your final answer.