In the future, each country in the world produces its Olympic athletes via cloning and strict training
programs. Therefore, in the finals of the 200 m free, there are two indistinguishable athletes from each
of the four countries. How many ways are there to arrange them into eight lanes?
1. We need to arrange 8 athletes into 8 lanes, where there are 2 indistinguishable athletes from each of the 4 countries.
2. First, we choose 2 lanes out of 8 for the first country's athletes. The number of ways to do this is given by the binomial coefficient:
   \[
   \binom{8}{2} = \frac{8!}{2!(8-2)!} = \frac{8 \times 7}{2 \times 1} = 28
   \]
3. Next, we choose 2 lanes out of the remaining 6 lanes for the second country's athletes. The number of ways to do this is:
   \[
   \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15
   \]
4. Then, we choose 2 lanes out of the remaining 4 lanes for the third country's athletes. The number of ways to do this is:
   \[
   \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6
   \]
5. Finally, the last 2 lanes are automatically assigned to the fourth country's athletes. There is only 1 way to do this:
   \[
   \binom{2}{2} = \frac{2!}{2!(2-2)!} = 1
   \]
6. Therefore, the total number of ways to arrange the athletes is the product of these individual choices:
   \[
   28 \times 15 \times 6 \times 1 = 2520
   \]

The final answer is $\boxed{2520}$