I always like to begin projects with simple shapes.  Think about what simple shapes make up the object you want to make and start with those.  In this case we want to start with a rectangle and a circle.  I used the combine tool to unite the two after lining up the circle so that half is overlapped at the top of the rectangle.

Next we need to consider the diameter of the door knob base.  I measured the knob in my house, but you may need to double check your own and modify accordingly.  Mine are about 1.25 inches

Of course, the knob is much larger than the part we will hang the door hanger from.  Because of this it doesn't make sense to have a huge cut out for the knob.  The better design is to cut out one side of the hanger.  To do this let's use some rectangles to make some cuts.  Use the combine tool to subtract.

This will leave an island that needs to be removed by using rectangles to cover it and then use the combine tool to subtract the section away.

The last step is to round over the end of the hook part that goes over the door knob.  To do this we can simply use a circle and unite it to the rest of the hanger design.