The paper presents the reduction of the boundary-value problem related to a particular diffraction problem to a matrix-valued Wiener-Hopf equation. The diffraction problem in question is the diffraction of a plane electromagnetic wave by an impedance loaded parallel plate wave guide formed by a two-part impedance plate and a perfectly conducting half-plane. The authors represent the solution of the resulting Wiener-Hopf equation in terms of the solution of two infinite systems of linear algebraic equations. These systems are treated numerically and the influence of the physical parameters of the waveguide on the diffraction phenomenon is analyzed graphically.