The GCF of the three terms is $\displaystyle{2}{x}\usepackage{cmbright}\Huge\$ , so $\displaystyle{2}{{x}}^{{3}}+{6}{{x}}^{{2}}+{4}{x}={2}{x}{\left({{x}}^{{2}}+{7}{x}+{12}\right)}\usepackage{cmbright}\Huge\$ .

Factor by grouping:

$\displaystyle{2}{x}{\left({{x}}^{{2}}+{7}{x}+{12}\right)}={2}{x}{\left({{x}}^{{2}}+{3}{x}+{4}{x}+{12}\right)}={2}{x}{\left({x}+{3}\right)}{\left({x}+{4}\right)}\usepackage{cmbright}\Huge\$