From the equation,
[tex]\begin{gathered} 4x^2+bx-3 \\ a=4,\text{ b=b, c=-3} \end{gathered}[/tex][tex]\begin{gathered} \text{Following the hint provided, the multiplication of 'a' and 'c' is ;} \\ 4\times-3=-12 \end{gathered}[/tex][tex]\begin{gathered} The\text{ factors are} \\ +12\text{ and -1} \\ +6\text{ and -2} \\ +4\text{ and -3} \end{gathered}[/tex][tex]\begin{gathered} \text{Addition of these factors to get 'b' will be:} \\ +12x-1x\text{ = 11x} \\ +6x-2x\text{ = 4x} \\ +4x-3x\text{ = 1x} \end{gathered}[/tex]Hence, the possible values of b are 11,4 and 1, Option C