1. Convert mixed numbers to improper fractions: $$8\frac{1}{25} = \frac{201}{25}$$, $$7\frac{4}{5} = \frac{39}{5}$$.
2. Find a common denominator (25): $$\frac{39}{5} = \frac{39 \times 5}{5 \times 5} = \frac{195}{25}$$.
3. Subtract the fractions: $$\frac{201}{25} - \frac{195}{25} = \frac{6}{25}$$.