2 2/49 * 24/125 : 15/16 * 1/48 = ?

First, convert the mixed number to an improper fraction:
$$2 \frac{2}{49} = \frac{2 \cdot 49 + 2}{49} = \frac{98 + 2}{49} = \frac{100}{49}$$
Now the expression is:
$$\frac{100}{49} \cdot \frac{24}{125} : \frac{15}{16} \cdot \frac{1}{48}$$
Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite the expression as:
$$\frac{100}{49} \cdot \frac{24}{125} \cdot \frac{16}{15} \cdot \frac{1}{48}$$
Now, multiply the fractions:
$$\frac{100 \cdot 24 \cdot 16 \cdot 1}{49 \cdot 125 \cdot 15 \cdot 48} = \frac{4 \cdot 24 \cdot 16}{49 \cdot 5 \cdot 15 \cdot 48} = \frac{4 \cdot 24 \cdot 16}{49 \cdot 5 \cdot 15 \cdot 2 \cdot 24} = \frac{4 \cdot 16}{49 \cdot 5 \cdot 15 \cdot 2} = \frac{64}{49 \cdot 5 \cdot 30} = \frac{64}{49 \cdot 150} = \frac{64}{7350} = \frac{32}{3675}$$

Answer: 32/3675