Step 1: Let's recall that a segment bisector is a ray or segment which cuts another line segment into two equal parts.
Step 2: Upon saying that, we have:
DS = SE
Step 3: Replacing with the equation we have to solve for x:
4x + 12 = 8x - 8
4x - 8x = - 8 - 12
-4x = -20
Dividing by - 4
-4x/-4 = -20/-4
x = 5
Step 4: If x = 5, let's find the length of DS and SE:
4 * 5 + 12 = 8 * 5 - 8
20 + 12 = 40 - 8
32 = 32
Step 5: x = 5 and DS/SE = 32