The first potter's rate is $\displaystyle\frac{{15}}{{5}}\usepackage{cmbright}\Huge\$ or 3 mugs per hour. The second potter's rate is $\displaystyle\frac{{12}}{{3}}\usepackage{cmbright}\Huge\$ or 4 mugs per hour. Their combined rate is 7 mugs per hour. So if $\displaystyle{t}=\usepackage{cmbright}\Huge\$ the amount of time, in hours, needed for the two potters to produce 63 mugs, then:

$\displaystyle{7}=\frac{{63}}{{t}}\usepackage{cmbright}\Huge\$ , so $\displaystyle{7}{t}={63}\usepackage{cmbright}\Huge\$ , and $\displaystyle{t}={9}\usepackage{cmbright}\Huge\$