"Six more than a number doubled is equal to twice a
number plus three"

Given parameters:

  This is a word problem. To solve problems, it is best to interpret sentence by sentence;

   Six more than a number doubled;

      let the number  = y ;

      so  we have 2(y + 6)

    equal    =

     twice a  number plus three;

      let the number be Z;

           2Z + 3

The complete expression is thus;       2(y + 6) = 2Z + 3

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2