39 people can build a road in 12 days working 5 hours a day. How many days will it take 30 people to build the same road if they work 6 hours a day?

The total work is constant regardless of the number of people or hours. We can express work units as (number of people) $\times$ (days) $\times$ (hours per day).
In the first scenario:
Number of people ($M_1$) = 39
Days ($D_1$) = 12
Hours per day ($H_1$) = 5

$$\text{Total Work Units} = M_1 \times D_1 \times H_1 = 39 \times 12 \times 5$$ $$\text{Total Work Units} = 39 \times 60 = 2340 \text{ work units}$$

In the second scenario:
Number of people ($M_2$) = 30
Hours per day ($H_2$) = 6
Days ($D_2$) = ? (This is what we need to find)
The total work units remain the same.

$$\text{Total Work Units} = M_2 \times D_2 \times H_2$$ $$2340 = 30 \times D_2 \times 6$$

$$2340 = 180 \times D_2$$ $$D_2 = \frac{2340}{180}$$ $$D_2 = \frac{234}{18}$$ $$D_2 = 13$$

So, 30 people working 6 hours a day can complete the work in 13 days.

The final answer is $\text{} 13 \text{ days} \text{}$