A car moving on a straight road covers one third of a certain distance with 20 km/h and rest with 60 km/h. The average speed is:

Let the total distance be $D$.
The car covers the first part of the distance ($d_1$) with speed $v_1$.

$$d_1 = \frac{1}{3}D$$ $$v_1 = 20 \text{ km/h}$$

The car covers the remaining distance ($d_2$) with speed $v_2$.

$$d_2 = D - \frac{1}{3}D = \frac{2}{3}D$$ $$v_2 = 60 \text{ km/h}$$

The formula for time is $t = \frac{\text{distance}}{\text{speed}}$.
Time for the first part ($t_1$):

$$t_1 = \frac{d_1}{v_1} = \frac{\frac{1}{3}D}{20 \text{ km/h}} = \frac{D}{3 \times 20} \text{ h} = \frac{D}{60} \text{ h}$$

Time for the second part ($t_2$):

$$t_2 = \frac{d_2}{v_2} = \frac{\frac{2}{3}D}{60 \text{ km/h}} = \frac{2D}{3 \times 60} \text{ h} = \frac{2D}{180} \text{ h} = \frac{D}{90} \text{ h}$$

Total time $T = t_1 + t_2$.

$$T = \frac{D}{60} + \frac{D}{90}$$

To add these fractions, find a common denominator, which is 180.

$$T = \frac{3D}{180} + \frac{2D}{180} = \frac{3D + 2D}{180} = \frac{5D}{180} = \frac{D}{36} \text{ h}$$

The formula for average speed is $\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$.

$$\text{Average speed} = \frac{D}{T} = \frac{D}{\frac{D}{36}}$$ $$\text{Average speed} = D \times \frac{36}{D} = 36 \text{ km/h}$$

The average speed is 36 km/h. This corresponds to option (D).

The final answer is $\text{36 km/h}$.