Let the eccentricity of the hyperbola \( H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) be \( \sqrt{\frac{5}{2}} \) and length of its latus rectum be \( 6\sqrt{2} \). If \( y = 2x + c \) is a tangent to the hyperbola \( H \), then the value of \( c^2 \) is equal to:
