I think it's the right time for you to explore and play with variables.
I'll give you a bit of hint, and will let you try out. Besides, I don't know what type of game are you making. But anyway:
You want the next box to Start moving (after the previous box stops) provided that a Key was pressed in between the tween. Correct? For this, you can merge my solution with that of Kyatric.
You'll have two variables (Boolean): Tweening, and keyPressed (default: False)
That keyPressed variable will set true whenever a Key is pressed and it will remember (stay as true) that the key was pressed while the box was moving despite the actual key is released.
Then, "On Tween Finished" you should also check with another condition (is keyPressed?), if yes, then it should call the Function to start the next box Tween. (or you can do as I did, select whichever you want to move, by Picking).
Important: keyPressed should be set as False as soon as the box starts its Tween.