We present an efficient approach to study the spectra and eigenstates for the model describing six multiphoton processes in the presence of bosonic modes without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter λ for a class of models describing the six-mode multiphoton processes. The parameter is determined by the roots of a polynomial and is solvable analytically or numerically.