1. **Stating the problem:** Given a geometric figure with points A, B, C, D, E, and P, where angles at B and C are 60°, and segment BE = 3a, we are asked to find the length of BC. 2. **Understanding the problem:** We have segments AB, BC, CD, and BE with given relationships and angles. The goal is to find BC. 3. **Key information:** - Angles at B and C are 60°. - BE = 3a. - The segments AB, BC, CD are related to W and 2W. 4. **Using triangle properties:** Since angles at B and C are 60°, triangles involving these points are equilateral or have special properties. 5. **Express BC in terms of a:** Given BE = 3a and the geometry, BC corresponds to a segment related to BE. 6. **Conclusion:** From the given data and the 60° angles, BC = 2a. **Final answer:** $$BC = 2a$$