Based on how the triangle looks and the directions given, you know that this is a right triangle.
You can use the Pythagorean Theorem, which is a^2 + b^2 = c^2, with c being the hypotenuse. If you plug in the values, you get
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
√100 = √c^2
c = 10
This means that Robert traveled 10 kilometers on the way back home, HOWEVER, it asks for the round trip distance. He traveled 14 km on the way there and 10 km on the way back, which means the round trip distance is 24 km.
I hope this makes sense!