Correct. Factor the numerators and denominators. Regroup so that the common factors on top and bottom are in one fraction. This can be reduced to 1. Multiply the simplified expressions.

$\displaystyle\frac{{2}}{{{3}{{x}}^{{2}}}}\cdot\frac{{{12}{{x}}^{{3}}}}{{14}}=\frac{{2}}{{{3}\cdot{{x}}^{{2}}}}\cdot\frac{{{2}\cdot{2}\cdot{3}\cdot{{x}}^{{2}}\cdot{x}}}{{{2}\cdot{7}}}=\frac{{{2}\cdot{3}\cdot{{x}}^{{2}}}}{{{2}\cdot{3}\cdot{{x}}^{{2}}}}\cdot\frac{{{2}\cdot{2}\cdot{x}}}{{7}}\usepackage{cmbright}\Huge\$

$\displaystyle={1}\cdot\frac{{{4}{x}}}{{7}}=\frac{{{4}{x}}}{{7}}\usepackage{cmbright}\Huge\$

The missing numerator is $\displaystyle{4}{x}\usepackage{cmbright}\Huge\$ .