The eccentricity of an ellipse \( E \) with centre at the origin \( O \) is \( \dfrac{\sqrt{3}}{2} \) and its directrices are \( x = \pm \dfrac{4\sqrt{6}}{3} \). Let \( H : \dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1 \) be a hyperbola whose eccentricity is equal to the length of semi-major axis of \( E \), and whose length of latus rectum is equal to the length of minor axis of \( E \). Then the distance between the foci of \( H \) is:
