Codes PO303, PO430, P3497, PO300, PO306

Hello. The code P3497 is causing the other codes. First of all, check the level of the engine oil, make sure it's up to where it should be, the code has to do with the Valve-Pause System (basically cylinder deactivation to save on gas mileage). The ECM (engine computer) can activate certain oil pressure solenoids to close the intake and exhaust valves on one side of the engine. In your case Bank 2, which is why you are getting misfire codes for cylinders 3 and 6 because they are on the same side of the engine. There is a Technical Service Bulletin on this. The ECM monitors the oil pressure to determine which cylinders have been shut down. Most likely you have a failed oil pressure solenoid. You're getting the P0430 because of the misfiring cylinders. Below is the Technical Service Bulletin information.
Since you were able to shut down the car and make it home, it means you are going to have worse problems soon if the issue is not addressed. If you haven't changed your oil or it's low, it can cause this as well. On these systems you must keep up with your oil changes and keep the correct type of oil in the engine as well.
Since you are getting misfire codes, I don't think this is just a failure in the Rocker Arm oil pressure switch. I think it's going to be more of an issue with the Rocker Arm oil control valve or a failed ECM, But the failed control valve is more likely. I experienced this myself on my Honda when I owned it.
But check your oil first, and if it has not been changed in a long time, you can try that first. If the code continues to show up, you'll have to head to the dealership so they can figure out what has failed.
If you have a scan tool that can show you live data, you can try the diagnostics on page 2 below. If not, it will have to diagnosed by someone who can watch live data and see what the ECM is detecting.

15% level? Can you check it with the dipstick? if that's saying your oil level is low, I'm not sure exactly what they mean by 15%, but I would open the hood and take a paper towel and check the oil dipstick and see if it is at the full level. Do this before you drive or even start the car. Go to Step 8 on the guide below.

https://www.2carpros.com/articles/how-to-change-engine-oil-and-filter

Okay, but a low oil level can set these codes as well. Or contaminated oil. Oil eventually mixes with some gasoline because of blow by gases past the piston rings, that's why it's important to change your oil at the suggested intervals.
Where do you get your oil changed? Or do you do it by yourself?

Okay. I would make sure that they put the correct type of oil that is recommended for your car in the engine. The owner's manual in your glovebox will have the correct type of oil that is supposed to be used in your car. Some of those oil change places just put in what they have in stock. They don't bother to carry every type of oil, whether it be synthetic or regular, of even the correct viscosity (10-w30. 5-w30, etc, ) and with these newer systems it's important to have the correct oil in the engine.
That being said, there have been issues with these systems as well, that's why Honda put out that Technical Service Bulletin. Once they start seeing an issue occur consecutively, they will put out a Recall or a Bulletin about the issue.

So, you are probably down almost a whole quart of oil. Take a look in your glove box owner's manual to see what kind of oil Honda recommends for your car. Add enough to get it up to the full line, erase the codes and see which ones come back. If there is an issue with a pressure sensor or solenoid a code will come back. It should come back after only one drive I believe. It depends on the code setting criteria for that particular system. Try not to go too far from home, but if you can get to a point where you're at a light cruise, the valve pause (cylinder deactivation) should turn on or attempt to. If the P3497 comes right back, then it needs to have the pressure sensor and the rocker arm oil control solenoid checked. After that's repaired it should take care of the other codes. You just don't want to cause any damage to the catalytic converter (P0430).

I wanted to show you this, here is a small list of "real repairs" due to this code p3497. Just so you can get an idea of what actually happens. The last Honda I had a code for was a similar problem and I diagnosed it as the oil pressure solenoid on the back of the engine. On a road test it was stalling out on the highway doing the same thing yours is probably doing. It's listed here as the VTEC solenoid, some people call it variable valve timing but it's really not what it is. It's a valve closing system to help save on gas.

That's great news, just keep an eye on the oil level for the next couple of weeks to make sure it is staying up where it should be. It was the low oil level that was causing the valve pause system to malfunction. Hopefully there won't be any other issues with it. I'm surprised it was that low, it's a bit concerning, so if you notice in the next week or two that it's dropping off let him know. I'm assuming you don't have a puddle of oil in your driveway.

If you notice it getting low and there's no leaks yet have him check the PCV system, If its clogged up and not free flowing it can lead to oil being burned by the engine and will also cause leaks to eventually start.