Correct Answer: $7$

Solution : Given: $\frac{-7} { \left[5 + \frac{1}{2} - \left\{4 + \left(\frac{4}{\frac{2}{4}}\right) + \left(\frac{4}{\frac{4}{2}}\right) \right\}\right]}$
= $\frac{-7} { \left[5 + \frac{1}{2} - \left\{4 + \left(\frac{8}{4}\right) + \left(\frac{4}{8}\right) \right\}\right]}$
= $\frac{-7} { \left[5 + \frac{1}{2} - \left\{4 + 2 + \frac{1}{2} \right\}\right]}$
= $\frac{-7} { \left[5 + \frac{1}{2} - 6.5\right]}$
= $\frac{-7} { (5.5 - 6.5)}
$
= $\frac{-7}{-1}$
= $7$
Hence, the correct answer is $7$.