There are multiple methods to do this.
If you're running AutoCAD older than 2022, one way is to open each dwg in a separate session of AutoCAD. Then you can position both AutoCAD windows side by side so you can see both dwgs simultaneously.
If you're running AutoCAD 2022 and newer, make sure system variable SYSFLOATING is set to 1.
Then with both dwgs opened, you should see each of the drawings shown as tabs along the top.
Click and hold the DWG tab you want to move.
Drag it downward and away from the row of drawing tabs.
Keep dragging until the drawing becomes a separate floating window.
Now you can resize the AutoCAD window along with the separate floating DWG window side by side.
You're ready to select the objects you want to copy (Ctrl+C) from one dwg and paste (Ctrl+V) into the other dwg.