If the eccentricity of the standard hyperbola passing through the point (4,6) is 2,

Let us Suppose equation of hyperbola is

$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$

$\mathrm{e}=2 \Rightarrow \mathrm{b}^{2}=3 \mathrm{a}^{2}$

passing through $(4,6) \Rightarrow \mathrm{a}^{2}=4, \mathrm{~b}^{2}=12$

$\Rightarrow$ equaiton of tangent

$x-\frac{y}{2}=1$

$\Rightarrow 2 x-y-2=0$