Hello: I have the same problem with the code P0420 that was found on a diagnostic from the gas station, but they didn't do a full diagnostic. I took it to Midas and they did a full diagnostic and found the same code but nothing else. That code refers to the catalytic converter and they said that it was failing or starting to fail. The catalytic converter takes care of your emissions through your exhaust so that you can pass emissions depending on the state you live in. Some states do not require emissions tests. Most states do require that.
Since you have the code P0420, which is a bad code and refers to the catalytic converter, please get a 2nd opinion (which I did) and get it checked out the right way...through the computer and full diagnostic on the Check Engine Light. If the same code comes up, they will replace the catalytic converter, but it will be very pricey depending on where you go. Always shop around for the best price of that.
Also, tell each shop you call what code you got from the previous diagnostic, and ask them to explain it if they can. If you have to drive your car there to show them the bill and the code(s) that you got, then they will tell you what they mean and why.
To get a catalytic converter replaced will cost you between $700-900 depending on where you go. Beware of gas stations that will charge you double to triple for the labor costs. The gas station near my house was going to charge me close to $2,000 for to replace the converter, when in fact you can get it for a cheaper price from more reputable mechanics. Also, please avoid the dealership to have them replace it. You can have them do a full diagnostic on the car, which I had done, and they told me the code, which was P0420 (the dreaded catalytic converter).
Fortunately, this converter is the original part from when I bought the car as brand new. So 9 years it took to start to fail, which is pretty darn good.
Rule of thumb: If you drive your vehicle a lot and sometimes long distances, you can wear out the catalytic converter very quickly...mostly between 2-3 years if you do drive it a lot. If you don't drive it a lot, like I do, then you can have it last close to 10 years or so, like I did. My previous car, I traded it in after 10 years and 45,000 miles and I didn't have to have the converter replaced, because technically the car was not driven a lot, like other vehicles are.
If you have the O2 sensor (oxygen sensor) replaced, then it will cost you between $120-$150 per sensor. And that usually is separate from the catalytic converter. But the whole bill can run you between $1,000-$1,200 depending if you need the O2 sensor replaced or not. The only way to know if it needs to be replaced is that if the Check Engine code(s) say that or not.
Be aware of what mechanic you are talking to. Some gas station mechanics will not educate you on how the car works, and they will "rush" through the job to get your money and then go onto something else. That was why I shopped around for this, because it is a very major piece to the car, and I wanted to get it done right.
Good luck with who you want to do the job. And hope you get it done on the cheap side. At least I am saving close to $1,200 since I didn't choose a gas station near my house to do it. I chose a very reputable national chain, such as Midas, to do it.
I would advise you very highly to take it to Midas. This catalytic converter stuff is right up their alley and they know how to deal with exhaust systems as well as mufflers.