Starting from a point, Karan moves $6\text{km}$ in one direction and then $8\text{km}$ at a right angle to his initial path. What is the direct distance between his starting point and his final position?

The path taken by Karan forms a right-angled triangle, where the two perpendicular sides are $6\text{km}$ and $8\text{km}$.
The direct straight-line distance between the starting point and the final position represents the hypotenuse ($d$) of this right-angled triangle.

Using the Pythagoras theorem:

$$d^2=6^2+8^2$$

$$d^2=36+64$$

$$d^2=100$$

$$d=\sqrt{100}=10\text{km}$$

Therefore, the direct distance is $10\text{km}$.