Correct. No, the lines are not parallel. If $\displaystyle{3}{x}+{2}{y}={4}\usepackage{cmbright}\Huge\$ , then $\displaystyle{2}{y}=-{3}{x}+{4}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}=-\frac{{3}}{{2}}{x}+{2}\usepackage{cmbright}\Huge\$ ; this means the first line has a slope $\displaystyle-\frac{{3}}{{2}}\usepackage{cmbright}\Huge\$ . If $\displaystyle{2}{x}+{3}{y}={6}\usepackage{cmbright}\Huge\$ , then $\displaystyle{3}{y}=-{2}{x}+{6}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}=-\frac{{2}}{{3}}{x}+{2}\usepackage{cmbright}\Huge\$ , meaning that the slope of the second line is $\displaystyle-\frac{{2}}{{3}}\usepackage{cmbright}\Huge\$ . Since the lines have different slopes they are not parallel.