One way is to use fsolve() from optimization toolbox
fun = @(x, y) [-2*x.^2+3*x.*y+4*sin(y)-6; ...
sol = fsolve(@(x) fun(x(1), x(2)), rand(1, 2));
x = sol(1);
y = sol(2);
Note: due to periodic functions in you equations, there seems to be multiple solutions.
Another approach is to use vpasolve from symbolic toolbox
syms x y
eq1 = -2*x.^2+3*x.*y+4*sin(y)==6;
eq2 = 3*x.^2-2*x.*y.^2+3*cos(x)==-4;
eq = [eq1; eq2];
sol = vpasolve(eq);
x = sol.x;
y = sol.y;