Evaluate the expression: 105/32 * (320/21 + 864/15)

First, find the least common multiple (LCM) of the denominators 21 and 15.
$21 = 3 \times 7$
$15 = 3 \times 5$
LCM$(21, 15) = 3 \times 5 \times 7 = 105$.

Convert the fractions to have a common denominator of 105:

$$\frac{320}{21} = \frac{320 \times 5}{21 \times 5} = \frac{1600}{105}$$ $$\frac{864}{15} = \frac{864 \times 7}{15 \times 7} = \frac{6048}{105}$$

$$\frac{105}{32} \left( \frac{7648}{105} \right)$$

Notice that 105 in the numerator and 105 in the denominator cancel each other out.

$$\frac{1}{32} \times 7648 = \frac{7648}{32}$$

$$\frac{7648}{32} = 239$$

The final answer is 239.