The spin-1/2 quantum transverse Ising model, defined on a ladder structure, with nearest-neighbor and four-spin interaction on a plaquette, is studied by using exact diagonalization and finite-size-scaling procedures. The quantum phase transition between the ferromagnetic and paramagnetic phases has been obtained in the thermodynamic limit. The critical transverse field decreases as the antiferromagnetic four-spin interaction increases, and reaches a multicritical point. However, the exact diagonalization approach was not able to capture the essence of the dimer phase beyond the multicritical transition.