If the equation   has 3 real roots, then

$$\begin{gathered} f\left(x\right)=2x^3-3x^2-12x+k \\ {f}^{\mathrm{\prime }}\left(x\right)=6x^2-6x-12=6(x+1)(x-2) \\ {f}^{\mathrm{\prime }}\left(x\right)=0\Rightarrow x=-1,2 \end{gathered}$$

$\text{ For }3\text{ real roots maximum }f\left(x\right)>0\text{ and minimum }f\left(x\right)<0$
$$\begin{gathered} f(-1)>0\Rightarrow k+7>0,k>-7 \\ f\left(2\right)<0\Rightarrow k-20<0,k<20 \\ \therefore -7<k<20 \end{gathered}$$