More like an addressable latch, witch I mentioned earlier.
As I read that then for N output pins driving your bar graph you need N+1 pins on your processor.
That is one pin for each of the outputs you want to drive and the one more pin to clock the data into the latch. This is no different from using just the existing output pins but you need one more for the clock. You have no need to connect the output enable input to an Arduino pin, you can permanently enable the pins.
So you are still not getting the vital point that this circuit is absoloutly useless for getting more outputs from your processor, and also totally unnecessary. If your teacher can't see that then he does not know his subject very well. (Or substitute her instead of him.)