In this talk, I will present the boundary regularity of solutions to a class of variable-exponent gradient degenerate mixed fully nonlinear local-nonlocal elliptic Dirichlet problems. A crucial feature of the operators under consideration is that they degenerate on the set of critical points, $\mathcal{C}\text{:=}\,\{x: Du(x)=0\}.$ First, we establish the Lipschitz and H\older regularity of solutions using the Ishii-Lions viscosity method for the cases when the order of the fractional Laplacian, $s$ is within $\big({1}/{2},1\big)$ and $\big(0,{1}/{2}\big],$ respectively, under general conditions. Due to the inapplicability of the comparison principle for the equations under consideration, in general, the classical Perron`s method for the existence of a solution can not employed. However, by utilizing the Lipschitz/H\older estimates established and \enquote{vanishing viscosity} method, we prove the existence of a solution. Additionally, we prove interior $C^{1,\delta}$ regularity of viscosity solutions using an improvement of the flatness technique when $s$ is close enough to $1$ or $0.$ Furthermore, under suitable assumptions, we establish the H\older regularity of solutions up to the boundary.