$\displaystyle \frac{1}{2b^2+b}<\frac{1}{ab^2}$ iff $\displaystyle 2b^2+b>ab^2$. In the latter inequality, both sides are quadratic polynomials in b. I understand that this problem is formally about quantifiers, but essentially it is about comparing two quadratic functions. For this reason, if you need help with this, it would make sense to post the problem to pre-university Algebra or Pre-calculus subforums.