Để \(\left[m;2m-3\right]\subset\left(4;+\infty\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>4\\2m-3>m\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m>4\\m>3\end{matrix}\right.\Leftrightarrow m>4\)
\(\Leftrightarrow m\in\left(4;+\infty\right)\)