Here, R_P = 2R_E , ${\rho _E} = {\rho _P}$

Escape velocity of the earth,

${V_E} = \sqrt {{{2G{M_E}} \over {{R_E}}}} = \sqrt {{{2G} \over {{R_E}}}\left( {{4 \over 3}\pi R_E^3{\rho _E}} \right)}$
$= {R_E}\sqrt {{8 \over 3}\pi G{\rho _E}}$   ...(i)

Escape velocity of the planet

${V_P} = \sqrt {{{2G{M_P}} \over {{R_P}}}} = \sqrt {{{2G} \over {{R_P}}}\left( {{4 \over 3}\pi R_P^3{\rho _P}} \right)}$
$= {R_P}\sqrt {{8 \over 3}\pi G{\rho _P}}$   ...(ii)

Divide (i) by (ii), we get

${{{V_E}} \over {{V_P}}} = {{{R_E}} \over {{R_P}}}\sqrt {{{{\rho _E}} \over {{\rho _P}}}} = {{{R_E}} \over {2{R_E}}}\sqrt {{{{\rho _E}} \over {{\rho _E}}}} = {1 \over 2}$

$\Rightarrow {V_P} = 2{V_E}$