The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary

We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in ${\text{bC}}^n$. Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian manifolds with boundary that equipped locally conformal K"ahler metrics, provided a subsolution.