Wiktionary
vb. (context chiefly US slang English) care about; place value in; give a toss.
Usage examples of "give two hoots".
The man didn't give two hoots about convention if it meant her safety.
She didn't give two hoots about what happened to her bones when they were no longer securely encased in a working skin but knew from long experience with the Navajo that people got exceedingly testy when the graves of their ancestors were defiled.
Do you know, at the moment, I couldn't give two hoots about the prime minister, or long past murders, or whether Claudes disappear or not?
They don't give two hoots who handles the actual repairs as long as Dader supervises everything.
Rimmer was perfectly well aware that he was in the wrong plane of the wrong dimension of reality and, quite honestly, he didn't give two hoots.
He couldn't give two hoots in hell about the senator's opinions on the stock market.
At least you care about him, even if you don't give two hoots and a holler about your own skin.