What is the arc measure of dbe in degrees?

I'll do it the only way I can see. There are two angles there that look like they are right angles. One of them is labeled 4w + 4 and the other 4w+8. Obviously they cannot be equal to the same thing. 

So the only way is if they are slightly off being right angles, but they add up to 180 degrees.

4w + 4 + 4w + 8 = 180
8w + 12 = 180   Subtract 12 from both sides.
8w = 180 - 12
8w = 168 Divide by 8
w = 168 / 8 
w = 21 

4w + 4 = 4*21 + 4 = 88 There's an angle vertically opposite that is equal to 88 as well.
2w + 11 = 2 * 21 + 11 = 53
4w + 8 = 4*21 + 8 = 84 + 8 = 92

Now add what you have together.
88 + 88 + 92 + 53 = 321

The arc is DBE = 321o

This makes a lot of assumptions that may not be warranted. You have to run with it I suppose.