The GCF of the first two terms is $\displaystyle{2}{x}\usepackage{cmbright}\Huge\$ and the GCF of the last two terms is $\displaystyle-{1}\usepackage{cmbright}\Huge\$ . Factor those out. The resulting terms have a common factor $\displaystyle{\left({2}{x}-{3}\right)}\usepackage{cmbright}\Huge\$ .

$\displaystyle{4}{{x}}^{{2}}-{6}{x}-{2}{x}+{3}={2}{x}{\left({2}{x}-{3}\right)}-{1}{\left({2}{x}-{3}\right)}={\left({2}{x}-{3}\right)}{\left({2}{x}-{1}\right)}\usepackage{cmbright}\Huge\$