Arrange the numbers in descending order:
$$0.875,\frac{6}{8},0.872,\frac{13}{15}$$

To arrange the numbers in descending order (largest to smallest), let's convert the fractions into decimal values:
1. $0.875$
2. $\frac{6}{8}=\frac{3}{4}=0.750$
3. $0.872$
4. $\frac{13}{15}\approx 0.8667$

Comparing all the decimal values:

$$0.875>0.872>0.8667>0.750$$

Replacing them with their original forms:

$$0.875>0.872>\frac{13}{15}>\frac{6}{8}$$

Thus, the correct descending order is $0.875,0.872,\frac{13}{15},\frac{6}{8}$.