This is a factor of the first monomial, but it is not a factor of the second one. For each prime or variable they have in common, count how many times they have that factor in common. The GCF should have that many. The variable x occurs twice as a factor in $\displaystyle{6}{{x}}^{{2}}{{y}}^{{4}}\usepackage{cmbright}\Huge\$ , so $\displaystyle{{x}}^{{4}}\usepackage{cmbright}\Huge\$ should not be a factor of the GCF.