You may have started with the correct first step:

$\displaystyle{f{{\left({x}\right)}}}\cdot{g{{\left({x}\right)}}}={\left({4}{x}-{3}\right)}{\left(-{8}{x}+{1}\right)}\usepackage{cmbright}\Huge\$

However, it appears that you forgot the middle terms of the product. Be sure to use FOIL when multiplying two binomials. The correct answer is $\displaystyle-{32}{{x}}^{{2}}+{28}{x}-{3}\usepackage{cmbright}\Huge\$ .