What the hell would I know?

[Tinkerbell]

What the hell would I know?

??

[Ann1977]

What the hell would I know?

??

"the hell" is an intensifier. It makes the remark stronger.

"What would I know" becomes more emphatic by saying "What the hell would I know?"

It's like saying, "What on earth would I know?" or "What in heaven's name would I know?" These are all intensifiers.

Since "hell" is a very mild oath, it is the least polite of these forms. A sweet little old lady would not use this expression at a tea party.

[PROESL]

What the hell would I know?

??

It means, "Hey, don't ask me. I know nothing about it". or "Hey, don't ask me. I know nothing."

It could also be meant ironically, in which case the speaker would really mean, "I have something to say that's of value, but it looks you don't want to ask me about it or don't care to hear it. Suit yourself."

Yes, and as Anne said, "hell" is a kind of intensifier in this case. It's possible to use an offensive word in place of "hell". Some people have told me it's the first word they learn when they come here, which could be a sort of commentary on the negative side of US culture.