Answer: 139 Km.
Step-by-step explanation:
The question tells us that a planet A has an orbit period of 10 years and its circular orbit has a radius of 106 Km, whilst a planet B has an orbit period of 15 years (also assuming a circular orbit), both orbiting a nearby star.
This information allow us to use the Kepler's 3rd law, for the special case in which the orbit is circular.
Kepler's 3rd law, tells that there exist a direct proportionality between the square of the orbit period, and the cube of the orbit radius (in the more general case, with the cube of the semi-major axis of the elipse), for celestial bodies orbiting a same star.
(like Earth and Mars orbiting Sun).
So, for planet A and planet B (orbiting a same star), we can write the following:
(TA)²/ (TB)² = (rA)³ / (rB)³
Replacing by TA= 10 years, TB= 15 years, rA= 106 Km, and solving for Rb, we get RB= 139 Km.