Since the two terms have a common factor, then we factor and obtain $(x-2)((x-4)+(x-6))=0$. This gives $(x-2)(2x-10)=0$. Therefore, $x-2=0$ (which gives $x=2$) or $2x-10=0$ (which gives $x=5$). Therefore, the two roots of the equation are $x=2$ and $x=5$. Their product is 10.