$\displaystyle{\left|-{18}\frac{{3}}{{4}}\right|}+{\left|-{6}\frac{{2}}{{3}}\right|}={18}\frac{{9}}{{12}}+{6}\frac{{8}}{{12}}={24}+\frac{{17}}{{12}}={24}+{1}\frac{{5}}{{12}}={25}\frac{{5}}{{12}}\usepackage{cmbright}\Huge\$

Both addends are negative, so the sum is negative. The answer is $\displaystyle-{25}\frac{{5}}{{12}}\usepackage{cmbright}\Huge\$ .