Positive popularity for a teacher among students is built on respect, trust, and the teacher's effectiveness.
A teacher who is approachable and genuinely helps students solve their problems (both academic and, when appropriate, personal) is seen as supportive and caring.
This builds a strong, positive student-teacher relationship, which leads to respect and popularity.
Developing inappropriate intimacy (A) is unprofessional. Awarding marks unfairly (C) undermines respect. Punishing students (D) creates fear, not popularity.
Therefore, helping students solve their problems is the characteristic that makes teachers genuinely popular.