Answer
$\frac{1}{4}$
Work Step by Step
We have $$(\frac{5}{6} - \frac{5}{12}) - (\frac{1}{2})^2 * \frac{2}{3}$$
Doing the subtraction and the square power $$\frac{10-5}{12} - \frac{1}{4}*\frac{2}{3}$$
Doing the multiplication $$\frac{5}{12} - \frac{1}{6}$$
Finally solving the subtraction $$\frac{5-2}{12}= \frac{3}{12} = \frac{1}{4}$$