If the equation $2x^2+2hxy+6y^2-4x+5y-6=0$ represents a pair of straight lines, then the length of intercept on  the $x$-axis cut by the lines is equal to

The $x$-coordinates of the points of intersection of

the pair of lines given by $2x^2+2hxy+6y^2-4x+5y-6=0$ and 

$x$-axis are roots of the equation

$\begin{array}{l}2x^2-4x-6=0\text{ or, }{x}^2-2x-3=0\\ \Rightarrow (x-3)(x+1)=0\Rightarrow x=-1, 3\end{array}$

Hence, required length $=\left|x_1-x_2\right|=4,$