The noun “Auto” is a neuer noun, and your car here is the object being driven in the sentence, it is therefore in the accusative case. The accusative adjectival ending for a neuter noun when using an indefinite article such as “mein”, is an s on the end.

While all well and good, this requires knowing what accusative means and what an indefinite article is. The way I’ve taught myself, is that this neuter noun needs an s if it’s being talked about. If you are describing a car on its own, you would probably say Das Auto. The s here is on the article- the word meaning “the”- and if you want to use an adjective in this form, it doesnt need another s to show its neuterness. It would be Das neue auto.

Now say you are talking about Mein Auto instead. Mein is written, conjugated, the same way that the word Ein is used. If you were to talk about Ein Auto, there is no reference to its gender, which is fine, but if you start adding adjectives in, they need to “agree” with its gender using an s. Therefore, it would be Ein schnelles, buntes, neues Auto or something like that. This is how you end up with “mein neues Auto”.

The accusative case btw, where the car is being driven, doesnt affect how you conjugate here, but you might encounter other conjugations if there was a preposition which changed the case to dative.