The remainder when $x^4-6x^3+3x^2+26x-24$is divided by $x-4$ is

$f\left(x\right)=x^4-6x^3+3x^2+26x-24$

$f\left(x\right)$  is divided by $x-4$ then the remainder is $f\left(4\right)$

$\begin{array}{l}f\left(4\right)=4^4-6{\left(4\right)}^3+3{\left(4\right)}^2+26\left(4\right)-24\\ =256-384+48+104-24\\ =408-408\\ =0\end{array}$