<p>I’ll try to explain this as clearly as I can w/out a picture…</p>
<p>Let O and P denote the centers of the smaller and larger pulleys respectively. Draw radii OA and PB such that OA and PB are parallel, and both perpendicular to the straight section of the pulley (AB). Let D be on PB such that OD is parallel to AB. Then OPD is a right triangle, and you can determine that OP = 8, PD = 4. Then OPD is a 30-60-90 triangle, and OD = AB = 4 sqrt(3). Since that is the length of 1/2 of the straight part, the length of the straight part is 8 sqrt(3).</p>