$\text{ The absolute value of slope of common tangents to }$$\text{ parabola }{y}^2=8x\text{ and hyperbola }3x^2-y^2=3\text{ is }$

$\text{ Tangent to }{y}^2=8x\Rightarrow y=mx+\frac{2}{m}$ $\to \left(1\right)$$\left( \sin ce y=mx+\frac{a}{m}\right)$  

$given hyperbola equation is \frac{x^2}{1}-\frac{y^2}{3}=1$

$\text{ Tangent to }\frac{x^2}{1}-\frac{y^2}{3}=1\text{ is y}=mx\pm \sqrt{m^2-3}\text{ →}\left(2\right)$     $\left(\sin ce y=mx\pm \sqrt{a^2{m}^2-b^2}\right)$

 $\left(1\right), \left(2\right) represents same line$ .

  $\Rightarrow \frac{2}{m}=\sqrt{m^2-3}\Rightarrow 4 =m^2\left(m^2-3\right)$$\Rightarrow$$m=\pm 2$