Convert mixed numbers to improper fractions:
[tex]8\dfrac{3}{4}=\dfrac{8\cdot4+3}{4}=\dfrac{35}{4}\\\\2\dfrac{1}{6}=\dfrac{2\cdot6+1}{6}=\dfrac{13}{6}[/tex]
[tex]8\dfrac{3}{4}\div2\dfrac{1}{6}=\dfrac{35}{4}\div\dfrac{13}{6}=\dfrac{35}{4\!\!\!\!\diagup_2}\cdot\dfrac{6\!\!\!\!\diagup^3}{13}=\dfrac{(35)(3)}{(2)(13)}=\dfrac{105}{26}=4\dfrac{1}{26}\to\boxed{C.}[/tex]
