It's hard to see what the "heavy line segments" are in the picture, but I'm going to assume that it's the outsides of the rectangles NOT surrounding the shaded region.

If I'm correct, then the calculation is simple: The total perimiter of both rectanges is 24 and the perimiter of the shaded region is 3, so the perimiter of the non-shaded region is 24 - 3 = 21.

If the heavy line segments refer to some other parts of the picture, then please describe exactly what the question is asking for.