6. Let point $A(2,0)$, and $B$ be a point on the elliptical arc
$$
\frac{x^{2}}{4}+\frac{y^{2}}{3}=1(x>0, y>0)
$$

Draw a perpendicular from point $B$ to the $y$-axis, and let the foot of the perpendicular be $C$. Then the maximum value of the area of quadrilateral $O A B C$ is $\qquad$