English Grammar??

Both are correct: afford admits both verb forms, but the infinitive is far more usual.

I can't afford to buy a new car.

Aspara GusBoth are correct: afford admits both verb forms, but the infinitive is far more usual.

I was surprised by your answer, so I did some research.
COCA lists 88 matches for can't afford to buy and none for can't afford buying.
BNC lists 21 matches for can't afford to buy and none for can't afford buying

Blue JayI was surprised by your answer

I was going to say buying was wrong, but then I decided that I hear the construction often enough for it to be considered acceptable, at least in casual English.

You’ll find some results in COCA if you search afford + [vvg], including two instances of afford buying.

I agree that "I can't afford buying a car" is permitted in English, but the problem with it is that nobody ever says it, so it remains merely potential. I think we do learners a disservice if we tell them that "I can't afford buying a car" is not just plain wrong.

I checked the Corpus of Global Web-Based English and found 2792 matches for afford to buy and 54 for afford buying.
Evidently people use it occasionally, but I think afford buying needs to become more popular before we start recommending it.