Correct. Factor both terms, find their GCF, and factor it out of the expression.

$\displaystyle{24}{{x}}^{{3}}{y}={2}\cdot{2}\cdot{2}\cdot{3}\cdot{x}\cdot{x}\cdot{x}\cdot{y}\usepackage{cmbright}\Huge\$

$\displaystyle{48}{{x}}^{{2}}{{y}}^{{2}}={2}\cdot{2}\cdot{2}\cdot{2}\cdot{3}\cdot{x}\cdot{x}\cdot{y}\cdot{y}\usepackage{cmbright}\Huge\$

GCF $\displaystyle={2}\cdot{2}\cdot{2}\cdot{3}\cdot{x}\cdot{x}\cdot{y}={24}{{x}}^{{2}}{y}\usepackage{cmbright}\Huge\$

$\displaystyle{24}{{x}}^{{3}}{y}-{48}{{x}}^{{2}}{{y}}^{{2}}={24}{{x}}^{{2}}{y}{\left({x}\right)}-{24}{{x}}^{{2}}{y}{\left({2}{y}\right)}={24}{{x}}^{{2}}{y}{\left({x}-{2}{y}\right)}\usepackage{cmbright}\Huge\$

The missing exponent is 2.