I’d get a 4"-6" adaptor for the back of your 
use your 10’ hose (presuming it’s a better quality than the one provided) and don’t stretch it out all the way - put the fan at the end in the window. If you’re just placing the fan in an open window you might end up with blowback. You can either create a window with a hole in it (with whatever material is appropriate for your weather situation), or run the short hose from the fan around the corner of the window.
I’d also get/cut a blast gate for the back of your so you can shut off air getting back in when you’re not actively using it.
There have been some pretty fancy set-ups for high windows (search for basement window to get more)