Consider a hyperbola \( H : {x^{2}} - {2y^{2}} = 4 \). Let the tangent at a point \( P(4,\sqrt{6}) \) meet the x-axis at \( Q \) and latus rectum at \( R(x_{1},y_{1}), x_{1} > 0 \). If \( F \) is a focus of \( H \) which is nearer to the point \( P \), then the area of \( \triangle QFR \) is equal to:
