$$\frac{16}{15} - \frac{2}{3} + 6 + \frac{1}{2} - \frac{4}{5} = \frac{16}{15} - \frac{10}{15} + \frac{1}{2} - \frac{12}{15} + 6 = \frac{16 - 10 - 12}{15} + \frac{1}{2} + 6 = \frac{-6}{15} + \frac{1}{2} + 6 = -\frac{2}{5} + \frac{1}{2} + 6 = -\frac{4}{10} + \frac{5}{10} + 6 = \frac{1}{10} + 6 = 6\frac{1}{10} = 6,1$$
Ответ: 6,1.