The total neutron scattering cross section per molecule sigma(tot) of solid methane in phase II was measured for incident neutron energies 0.5 meV less than or equal to E(n)less than or equal to 10 eV in the temperature range 0.3 K less than or equal to T less than or equal to 19.5 K. The sigma(tot) depends on the rotational, translational and vibrational dynamics of the CH4 molecule and shows significant dependence both on E-n and T. For E-n above 165 meV, which corresponds to the first vibrational excitation level of CH4, the sigma(tot) is equal to 4 sigma(p)(A/(A + 1))(2) = 80 b with proton mass A = I and a bound cross section sigma(p) = 80 b of a single proton. For E-n approximate to 6.5 meV, which is approximately the librational energy of the CH4 rotor, sigma(tot) approaches 205 b at all temperatures. This is the cross section of a rigid H-4 tetrahedron rotating freely about its fixed center; the effective mass is A = 4. For E-n < 6.5 meV, the interference effects of scattering from different protons within the same molecule, sensitive to nuclear spin symmetry, are observed. sigma(tot)similar to[I(1+1)](T) with total nuclear spin of the ortho, meta, para molecules I = 2, 1 or 0, respectively. For E-n-->0, two limiting cases can be distinguished. At high temperatures, the lower limit of sigma(tot) is given by the bound (incoherent) cross section of four protons 4 sigma(p) = 320 b. At low temperature, where only the ground state with I = 2 is occupied, sigma(tot) = 8 sigma(p) = 640 b. The experimental data compare well with a quantum-mechanical model and the mass-tenser approximation. Multiple rotational-translational-vibrational scattering contributions are discussed also.