He walks $10$ miles at a rate of $2$ miles per hour,

$\therefore$ Time taken by him $= \frac{10}{2} = 5$ hours,

And he returns at a rate of $10$ miles per hour,

Time taken to travel 10 miles back $= 1$ hour

Hence, Total time of entire trip $ = 5+1 = 6$ hours.

**(C) is correct.**