What do you do when a soldier refuses to listen to your directions?

I once made the mistake of telling my TL "No!"
(Mind you this was in '77.)
The 'wall to wall' counseling I received from him and our SdLd made a lasting impression on me. Never again did I disrespect an NCO! Years later on he was my 1SG and we joked about.
Unfortunately, today, that is not an option!

Try being creative with some wit. Explain to him that if he doesn't get with it life is going to suck for him. Hard to buy expensive shit as an E-1

Back in the day, the NCO's would be smoking this clown to remind him of who is in charge.

There has been a huge push for todays Soldiers to wear safety ballistic glasses and even issues them to them. They have become mandatory to have them in a training environment in Basic and AIT. The issue is to get to the root of the reason the Soldier refused to take them off. Harsh punishment, UCMJ and ridicule do not solve the problem. Counseling the Soldier and listening helps to find out why and then you have to instill and reinforce why not. 13 weeks of Drill Sergeants enforcing a safety eyewear policy can really effect how the Soldiers thinks about removing his eyewear. On the other hand if the Soldier is just straight up belligerent about it and just wants to defy authority then it is time to use the power of the pen. Forcibly removing or damaging the Soldiers eyewear could have a negative effect like having the MP's pay you a visit and possibly setting yourself up for assault or criminal charges for destroying the eyewear. Remember you do this in front of your platoon or squad then this provides witnesses and also creates animosity. Do not do the wrong thing while trying to do the right thing.

Should have checked your troops prior to formation and educated your subordinate leaders first.

As a squad leader I have actually had a soldier who came to formation with sunglasses on. Being that I also wear lightly shaded sunglasses, first thing I ask is for the soldier to produce his prescription from a military doctor saying that he has light sensitivity and is allowed to wear them. If no prescription is in his possession, I then start with on the spot corrections and go forward from there.

Create a paper trail where you counsel the service member & after 3 or more THEN you pull UCMJ !

You punish the whole group until someone internally says"Hey dickhead take of the glasses" It's a Marine thing.

I'm curious to know how the situation was handled.

if the person giving the order was you then do you have a pattern of others disobeying your orders? if so then you could be the problem or at least part of it