When you rewrite the fractions with a common denominator, they must be equivalent to the original fractions. The numerators will not all remain unchanged.

$\displaystyle{4}\frac{{1}}{{4}}+{6}\frac{{7}}{{12}}={4}+{6}+\frac{{3}}{{12}}+\frac{{7}}{{12}}={10}\frac{{10}}{{12}}={10}\frac{{5}}{{6}}\usepackage{cmbright}\Huge\$

The correct answer is $\displaystyle{10}\frac{{5}}{{6}}\usepackage{cmbright}\Huge\$ feet.