Explanation

(d)
Equation of line perpendicular to $2x + y + 6 = 0\$and passes through origin is $x - 2y = 0$
$Now,\ point\ of\ intersection\ of\ 2x + y + 6 = 0\ and\ x - 2y = 0\ is\left( - \frac{12}{5},\ - \frac{6}{5} \right)$
$Similarly,\ point\ of\ intersection\ of\ x - 2y = 0\ and\ 4x + 2y - 9 = 0\ is\ \left( \frac{9}{5},\frac{9}{10} \right)$
Let the origin divide the line $x - 2y = 0$ in the ratio $\lambda:1$
$\therefore\ x = \frac{\frac{9}{5}\lambda - \frac{12}{5}}{\lambda + 1} = 0\ \Rightarrow \ \frac{9}{5}\lambda = \frac{12}{5}$
$\Rightarrow \ \lambda = \frac{12}{9} = \frac{4}{3}$