A soap bubble of the radius 3cm is formed inside another soap...

The formula of excess pressure inside the soap bubble is, $\dfrac{4T}{R}$ here $T$ is the surface tension and $R$ is the radius of the soap bubble,

$⇒ {P}_{0} + \dfrac{4T}{6} + \dfrac{4T}{3} = {P}_{0} + \dfrac{4T}{R}$

$⇒ \dfrac{1}{6} + \dfrac{1}{3} = \dfrac{1}{R}$$⇒ R = 2cm$.