$\text{a)}10,6-4\frac{2}{3}+16\frac{1}{15}=10\frac{6}{10}-4\frac{2}{3}+16\frac{1}{15}=10\frac{3}{5}-4\frac{2}{3}+16\frac{1}{15}=10\frac{9}{15}-4\frac{10}{15}+16\frac{1}{15}=22$  

$\text{b)}6\frac{1}{2}+\left(3\frac{1}{3}-\frac{1}{2}\right):2\frac{5}{6}-1\frac{3}{4}=6\frac{1}{2}+\left(3\frac{2}{6}-\frac{3}{6}\right):2\frac{5}{6}-1\frac{3}{4}=6\frac{1}{2}+2\frac{5}{6}:2\frac{5}{6}-1\frac{3}{4}=6\frac{1}{2}+1-1\frac{3}{4}=7\frac{1}{2}-1\frac{3}{4}=6\frac{6}{4}-1\frac{3}{4}=5\frac{3}{4}$  

$\text{c)}\frac{7,13}{2,75-1\frac{3}{5}}=\frac{7,13}{2,75-1\frac{6}{10}}=\frac{7,13}{2,75-1,6}=\frac{7,13}{1,15}=7,13:1,15=713:115=6\frac{23}{115}=6\frac{1}{5}=6,2$

$\text{d)}\frac{6,5+3\frac{1}{3}-0,5}{2\frac{1}{3}}=\frac{6\frac{1}{2}+3\frac{2}{6}-\frac{1}{2}}{2\frac{1}{3}}=\frac{6\frac{3}{6}+3\frac{2}{6}-\frac{3}{6}}{\frac{7}{3}}=\frac{9\frac{5}{6}-\frac{3}{6}}{\frac{7}{3}}=9\frac{2}{6}:\frac{7}{3}=9\frac{1}{3}\cdot \frac{3}{7}=\frac{{\sout{28}}^4}{{\sout{3}}^1}\cdot \frac{{\sout{3}}^1}{{\sout{7}}^1}=4$