The density of newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be :-

Acceleration due to gravity at the surface: $g = \dfrac{GM}{R^2}$
Mass in terms of density: $M = \dfrac{4}{3}\pi R^3 \rho$
$g = \dfrac{G \cdot \frac{4}{3}\pi R^3\rho}{R^2} = \dfrac{4}{3}\pi G\rho R$
So $g \propto \rho R$
According to the question $g_{planet} = g_{earth}$:
$\dfrac{4}{3}\pi G\rho_{planet}R_{planet} = \dfrac{4}{3}\pi G\rho_{earth}R_{earth}$
With $\rho_{planet} = 2\rho_{earth}$: $2\rho_{earth}R_{planet} = \rho_{earth}R$
$\Rightarrow R_{planet} = \dfrac{R}{2}$