To add fractions with unlike denominators, you must first rewrite them with a common denominator. You do not add the numerators and denominators.

$\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.