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

You can only salute an officer with your right hand anyway so the only way you could avoid that is try to get both articles in your left hand.

If your hands are full in the line of duty, I would say no. However, you should acknowledge the officer and render the greeting of the day.
Please note that this is only applicable if you CANNOT free your right hand and you are actually performing a task that requires it to be occupied: for example, you are carrying an artillery round or something else that requires two hands.

It might depend on the circumstances and surroundings when you encountered the officer, but I would suggest you find a way to carry both the mug and the binder with your left arm or hand and keep the right hand free for a salute. If the mug was full of liquid that might be a problem. There are times you have to carry something that requires both hands. Were I the officer you encountered I would acknowledge the greeting and carry on. The question comes down to how avoidable the circumstaces are that have your hands occupied. No person of any rank is incapable of common sense when circumstances make it appropriate.

It's common knowledge to AVOID any backlash from ANY OFFICER. Always keep that right hand empty!! Was the CSM wrong for telling you to render Salute to the CPT No he was not. Were you wrong for having both hands occupied No you was either. So I can only say to get a thermo with a handle or a loop ring. GOD SPEED!!

I pulled this out of AR600-25 Saluting and Officer. This is what it says : (see # 3) i. Salutes are not required to be rendered or returned when the senior or subordinate or both are—
(1) In civilian attire.
(2) Engaged in routine work if the salute would interfere.
(3) Carrying articles with both hands so occupied as to make saluting impractical.
(4) Working as a member of a detail or engaged in sports or social functions where saluting would present a safety
hazard.
(5) In public places such as theaters, churches, and in public conveyances.
(6) In the ranks of a formation.

Based on the soldiers hands having a binder and a mug , he or she, should have placed the mug to the left hand and the binder should have been placed under their arm, and a hand salute should been given and a good day greeting should also be rendered. There are always Circumstances of course should be taken in considerations and acknowledgments as well, such as if a soldier was carrying a crate using the use of both hands , then a greeting of acknowledging " Good Morning, Afternoon or Evening to the officer should be accepted and no reprimand to the soldier should be given.

If both hands are occupied, the proper action is to make eye contact with the officer and say, "Good morning/afternoon/evening, Sir/Ma'am!" A slight nod of the head is not inappropriate but not required. (I started out in the Air Force and defected to the Army a several years later. That's what the Air Force Customs and Courtesies Manual said when I started out in 1974, and it should be good for all services to the present day.)

Yes, and the CPT. Should've immediately corrected the dumbass CSM.

Dude, as much as I like coffee, never carry stuff with both hands if it doesn’t require it. If you’re carrying binders AND coffee, you’re wrong. Carry the binders out first, then go retrieve your coffee. If you have to walk the binders to another building, leave the coffee. I don’t know of any place I ever went into that did not have coffee.

What about holding an umbrella in right hand and carrying a heavy object in left hand?

Frankly, it depends what you were carrying. If you’re carrying a heavy object, such as a printer or such then no, it’s not necessary. If you’re carrying something that you can shift to your left hand, then definitely render salute.