smc

For two lines to be the same, their slopes must be equal and their intercepts must be equal. This is a necessary and sufficient condition. The slope of the first line is $\frac{-3}{b}$, while the slope of the second line is $\frac{c}{2}$. Thus, $\frac{-3}{b}=\frac{c}{2}$, or $bc=-6$. The intercept of the first line is $\frac{-c}{b}$, while the intercept of the second line is $6$. Thus, $6=\frac{-c}{b}$, or $-6b=c$. Plugging $-6b=c$ into $bc=-6$ gives $b(-6b)=-6$, or $b^2=1$. This means $b=\pm 1$ This in turn gives $c=\mp 6$. Thus, $(b,c)=(\pm 1,\mp 6)$, for two solutions, which is answer $\boxed{2}$