While these questions can be solved algebraically, it is often easier just to make up a distance. In this case, since we're using the numbers 3, 4, and 6, a distance of 12 will work nicely as it can be evenly divided by all three rates.

Average speed = total distance / total time

Total distance is just 3 * 12 = 36.

We'll need to calculate the time for each of the three trips using the $d=rt$ formula, which we can rewrite as $t=\frac{d}{r}$.

$t1 = 12/3 = 4$
$t2 = 12/6 = 2$
$t3 = 12/4 = 3$

That leaves us with $\frac{36}{(4+2+3)}$ or 4, so the answer is C.