Since you didn't say exactly how much space you have or how big a box you want to use. I want to know are you planning to place them all in the same dirt in the box??? If so, this may not work, Basil and Rosemary can grow quite big and tall, which will shade the lower
growing herbs. The area should recieve enough light though for the
plants not shaded by others...Also the mint could take over the box and choke some of the others out. I would try to arrange indiviual pots in a box and maybe rotate the pots or box weekly. If you have enough room maybe try using two
flower boxes with the lower
growing ones in the front of the window and the taller ones behind, just suggestions. Also the water requirments for all of those
plants are not the same which also could be a problem.