  Several recent studies reinforce the existence of a thick molecular disc in
galaxies along with the dynamically cold thin disc. Assuming a two-component
molecular disc, we model the disc of NGC 6946 as a four-component system
consisting of stars, HI, thin disc molecular gas, and thick disc molecular gas
in vertical hydrostatic equilibrium. Following, we set up the joint
Poisson-Boltzmann equation of hydrostatic equilibrium and solve it numerically
to obtain a three-dimensional density distribution of different baryonic
components. Using the density solutions and the observed rotation curve, we
further build a three-dimensional dynamical model of the molecular disc and
consecutively produce simulated CO spectral cubes and spectral width profiles.
We find that the simulated spectral width profiles distinguishably differ for
different assumed thick disc molecular gas fractions. Several CO spectral width
profiles are then produced for different assumed thick disc molecular gas
fractions and compared with the observed one to obtain the best fit thick disc
molecular gas fraction profile. We find that the thick disc molecular gas
fraction in NGC 6946 largely remains constant across its molecular disc with a
mean value of $0.70 \pm 0.09$. We also estimate the amount of extra-planar
molecular gas in NGC 6946. We find $\sim 50\%$ of the total molecular gas is
extra-planar at the central region, whereas this fraction reduces to $\sim
15\%$ at the edge of the molecular disc. With our method, for the first time,
we estimate the thick disc molecular gas fraction as a function of radius in an
external galaxy with sub-kpc resolution.
