Answer
$\frac{4}{21}$
Work Step by Step
A 2x2 determinant can be calculated as $ad-bc$, where a is the upper-left entry, b is the upper-right entry, c is the lower-left entry, and d is the lower-right entry.
Therefore, the value of the determinant is $(\frac{5}{7}\times\frac{2}{3})-(\frac{1}{3}\times\frac{6}{7})=\frac{10}{21}-\frac{6}{21}=\frac{4}{21}$