The quantum interference in a magnetic anisotropy model with four easy directions is studied within the spin coherent-state path-integral formalism. When the particle possesses half-integer spin, the Euclidean propagators reduce to that of a two-level system, indicating degeneracy of the states. The results are shown to be easily reproduced by introducing an effective tunnelling Hamiltonian, where the topological phase factor is properly incorporated. This effective-Hamiltonian approach is demonstrated to be equivalent to the dilute-instanton approximation. The discussions are then generalized to the N-well cases, and the symmetry of the effective Hamiltonian is analysed. Degeneracies of the tunnelling levels are discussed in detail. The quenching result obtained previously in the case of a double well can be recovered by a simple diagonalization of the effective Hamiltonian.