Incorrect. Apply the exponent 4 to each factor individually: $\displaystyle\frac{{{{4}}^{{4}}{{\left({{g}}^{{6}}\right)}}^{{4}}{{\left({{h}}^{{2}}\right)}}^{{4}}}}{{{{f}}^{{4}}{{\left({{g}}^{{2}}\right)}}^{{4}}}}\usepackage{cmbright}\Huge\$

Calculate $\displaystyle{{4}}^{{4}}\usepackage{cmbright}\Huge\$ and use the Power Rule for each variable. Then use the Quotient Rule: subtract the exponents of matching variables. The simplified expression is $\displaystyle\frac{{{256}{{g}}^{{16}}{{h}}^{{8}}}}{{{f}}^{{4}}}\usepackage{cmbright}\Huge\$

The correct answer is 16.