The area of the big rectangle
[tex]A_B=(3x+6)(2x+4)=(3x)(2x)+(3x)(4)+(6)(2x)+(6)(4)\\\\=6x^2+12x+12x+24=6x^2+24x+24[/tex]
The area of the small rectangle
[tex]A_S=(x-1)(x-3)=(x)(x)+(x)(-3)+(-1)(x)+(-1)(-3)\\\\=x^2-3x-x+3=x^2-4x+3[/tex]
The area of the shaded region
[tex]A=A_1-A_2\\\\A=(6x^2+24x+24)-(x^2-4x+3)=6x^2+24x+24-x^2+4x-3\\\\=5x^2+28x+21[/tex]
[tex]\boxed{Answer:\ D.\ 5x^2+28x+21}[/tex]
