An equation of tangent line at an inflection point of 

$f\left(x\right)=x^4-6x^3+12x^2-8x+3$ is 

$\begin{array}{l}{f}^{\mathrm{\prime }}\left(x\right)=4x^3-18x^2+24x-8,f^{\prime \prime }\left(x\right)=12x^2-36x\\ +24=12\left(x^2-3x+2\right)=12(x-1)(x-2),f^{\prime \prime }\left(x\right)\\ =0\Rightarrow x=1,2\end{array}$

If $x=1$ then $y=2\text{. }$If $x=2,y=3\text{. }$So equation of

tangent at (1, 2) is $y-2=f^{\mathrm{\prime }}\left(1\right)(x-1)=2(x-1)$. 

Equation of the tangent at (2, 3) is $y-3=f^{\mathrm{\prime }}\left(2\right)$

$(x-2)=0$