In hamiltonian circuit all vertices should be covered in the path without repetition of vertices. (and initial and final vertex should be same)
A. vertices are repeated no need to check.
B. A comes twice. Intuitively after AFC is traversed, you can note that we can either go to B side or ED side. So all vertices cannot be traversed after this.
D. No edge between E and B.
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C satisfies all condition. So C is correct.