Answer
$\dfrac{2}{3}$
Work Step by Step
The general formula to calculate the determinant of a $2 \times 2$ matrix which has 2 rows and 2 columns is
$D=\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc$
Now,
$D=\begin{vmatrix}\frac{2}{3}&\frac{1}{3}\\\frac{-1}{2}&\frac{3}{4}\end{vmatrix}=\frac{1}{2}+\frac{1}{6}=\dfrac{2}{3}$
