first off, we convert the mixed fractions to "improper", and then divide.
[tex]\bf \stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}}
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\stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}}
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\cfrac{14}{3}\div\cfrac{7}{6}\implies \cfrac{14}{3}\cdot \cfrac{6}{7}\implies \cfrac{14}{7}\cdot \cfrac{6}{3}\implies 2\cdot 2\implies 4[/tex]
