jmc

The area of a triangle is given by the formula $\frac{1}{2}bh$. Both $△ABD$ and $△ADC$ share the same height $AB$. Let $[ABD]$ be the area of $△ABD$ and $[ADC]$ be the area of $△ADC$. It follows that $\frac{[ABD]}{[ADC]}=\frac{\frac{1}{2}\cdot BD\cdot h}{\frac{1}{2}\cdot DC\cdot h}=\frac{BD}{DC}=\frac{4}{3}$. Thus, $[ADC]=\frac{3}{4}[ABD]=\frac{3}{4}\cdot 24=\boxed{18}$.