The given expression is
[tex]3\frac{1}{6}+5\frac{2}{3}[/tex]First, we transform each mixed number into a fraction
[tex]\begin{gathered} 3\frac{1}{6}=\frac{3\cdot6+1}{6}=\frac{18+1}{6}=\frac{19}{6} \\ 5\frac{2}{3}=\frac{5\cdot3+2}{3}=\frac{15+2}{3}=\frac{17}{3} \end{gathered}[/tex]We use these fractions to make the sum
[tex]\frac{19}{6}+\frac{17}{3}[/tex]Now, we use the following property
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex][tex]\frac{19\cdot3+17\cdot6}{6\cdot3}=\frac{57+102}{16}=\frac{159}{16}[/tex]