1. **Stating the problem:** We have a hexagon ABCDEF with conditions:\n- CD || AF\n- \(\angle CDE = \angle BAF\)\n- AB is perpendicular to BC (\(AB \perp BC\))\n- \(\angle E = 80^\circ\)\n- \(\angle C = 124^\circ\)\nWe need to find \(\angle AFE\).\n\n2. **Interpreting conditions:** \nSince \(\angle C = 124^\circ\), at vertex C, the internal angle is 124°. Also, \(AB \perp BC\) means \(\angle ABC = 90^\circ\).\n\n3. **Analyze angles at vertex B:** \nTriangle ABC has \(\angle ABC = 90^\circ\) and \(\angle C = 124^\circ\) is at C, but this angle is part of the hexagon, not triangle ABC. So next find \(\angle BCD\)=124° can be used to find positions or properties.\n\n4. **Using parallelism:** \nSince CD || AF and \(\angle CDE = \angle BAF\), corresponding angles are equal because of the parallel lines (CD and AF) and the transversal DE or AF.\nTherefore, \(\angle BAF = 124^\circ\).\n\n5. **Analyzing \(\angle E = 80^\circ\):** Given as internal angle at E.\n\n6. **Find \(\angle AFE\):**\nUsing sum of angles around point F, with parallel lines and known angles:\n\(\angle AFE = 180^\circ - \angle E = 180^\circ - 80^\circ = 100^\circ\) initially, but we need to check correctness with given data.\n\n7. **Sum of internal angles of hexagon:** \nSum = \((6-2) \times 180^\circ = 720^\circ\). Known angles: \(124^\circ (C), 80^\circ (E), 90^\circ (from AB \perp BC at B)\) plus the unknowns. Using this and equality \(\angle CDE = \angle BAF = 124^\circ\), one can calculate \(\angle AFE = 114^\circ\).\n\n**Final answer:** \(\boxed{114^\circ}\)