$$F = k * \frac{|Q_1 Q_2|}{r^2}$$ where r is the distance between the point charges and k is Coulomb Constant k=9 x 10^9Nm^2C^-2
If the charges are initially 3 cm apart and the resultant force between them is 144 times larger if charges are now 6 cm apart:
$$144 * F = k * \frac{|Q_1 Q_2|}{(6 \text{ cm})^2}$$
and also :
$$F = k * \frac{|Q_1 Q_2|}{(3 \text{ cm})^2}$$ then,
$$144k * \frac{|Q_1 Q_2|}{(3 \text{ cm})^2}= k * \frac{|Q_1 Q_2|}{(6 \text{ cm})^2}$$ which can be solved for k to become:
$$(144)*4*3^2=6^2 \newline3^4=$$
$$\boxed{k=12}$$
