The minimum  value of the function  $2\cos 2x-\cos 4x$ in $0\le x\le \pi$ is :

$$\begin{gathered} y=2\cos 2x-\cos 4x \\ \begin{array}{l}=2\cos 2x(1-\cos 2x)+1\\ =4\cos 2x{\sin }^{2}x+1\end{array} \end{gathered}$$

Obviously, ${\sin }^{2}x\ge 0$

Therefore, to be least value of $y,\cos 2x$ should be least i.e., - 1. Hence least value of $y$ is $-4+1=-3$.