The distance between object and its two times magnified real image...

Magnification, $m = \dfrac{v}{u} = - 2$

$⇒ v = - 2u \ldots \left(i\right)$

As,

$v - u = 45 \ldots \left(ii\right)$

$⇒ u = - 15cm$

Then, $v = 30cm$

From lens equation, we can write

$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} ⇒ \dfrac{1}{f} = \dfrac{1}{30} - \dfrac{1}{\left(- 15\right)}$

$⇒ f = + 10cm$