#### Answer

The escape speed from Planet Y is 14,140 m/s.

#### Work Step by Step

Let $M$ be the mass of Planet X.
Let $R$ be the radius of Planet X.
We can write an expression for the escape speed from Planet X.
$v_{esc,x} = \sqrt{\frac{2~G~M}{R}} = 10,000~m/s$
Note that radius of Planet Y is also $R$. Therefore Planet X and Planet Y have the same volume. Since the density of Planet Y is twice the density of Planet X, Planet Y has a mass of $2M$. We can find the escape speed from Planet Y.
$v_{esc,y} = \sqrt{\frac{2~G~(2M)}{R}}$
$v_{esc,y} = (\sqrt{2})~(\sqrt{\frac{2~G~M}{R}})$
$v_{esc,y} = (\sqrt{2})~(10,000~m/s)$
$v_{esc,y} = 14,140~m/s$
The escape speed from Planet Y is 14,140 m/s.