jmc

We only need to worry about the terms that multiply to have a degree of $2$. This would be given by the product of the terms $3x^2$ and $-4$ as well as the product of the terms $-2x$ and $-7x$. Thus, $$(3x^2)\times (-4)+(-2x)\times (-7x)=-12x^2+14x^2=2x^2,$$and the coefficient is $\boxed{2}$.