Do I need to render a salute to an officer when my hands are occupied?

Are you really using carrying a mug is an excuse not to salute? Tuck the binder under your armpit and carry the mug in your left hand

One can either focus on when one is not required to salute, and maybe continue to get grief, OR figure how to manage things so one can greet a superior appropriately. This is true in the military, where a hand salute is required, and in civilian life, where other forms of recognition show one to be savvy or a clod.

Had I been you—since I am averse to being yelled at by Sergeants Major for a second time—I would have tucked my binder under my left arm where I used to carry it in high school, put my mug in my left hand, and cheerfully saluted.

Now, had I a load of binders precariously balanced in each arm, I would have stopped, said “apologies I can’t salute with all these binders in my arms”, and hoped I wouldn’t catch grief again.

But better would have been to have some forethought, put those binders in a bag, leaving my hand free to open doors, greet friends, and salute as appropriate. And left my mug behind in saluting areas,

The right answer is in AR 600-25. No, you are not required. However, advice from a former enlisted career soldier. SGM especially CSM don't get promoted by merit. The only thing E9s are there for is to point out petty shit that no one else cares about. The CSM was showing off (kissing ass) for the CPT. Just take the ass chewing and be proud of it. In the military if your not pissing off some SGMs or CSMs your probably not doing much.

Slip the binder under your left arm and salute like you know you're supposed to.

In the Army, you can give the greeting of the day and you’re okay. Me, I’d put my stuff down.

If it is reasonable to put your coffee cup in your left hand with your binder. And render a salute then you do so. Exception if your carrying a larg box that you can not free up your right hand then no. But you schould give the greeting if the day. Such as good morning sir.

I probably would have put the cup in my left hand and the binder under my left arm if possible and saluted to avoid confrontation

I think that the officer should understand, but I am old school. I would say, put yourself in my position

The right answer is: Put the cup and binder into the left hand. That is if you can walk and chew gum for training to carry two items.

Come on. Stick the binder under your arm with the coffee cup and show proper respect. If you were carrying a 50 lb box with both hands it would be respectable to not salute.