The phrase "about exactly that" is correct and can be used in written English.
You can use it when you want to emphasize that something is precisely or specifically about a particular thing or topic. Example: "I want to write my essay about exactly that - the impact of climate change on our planet."
But, in the last fortnight, three plays have opened in London about exactly that subject.
If I was in your shoes, I'd be very curious about exactly that – the political will for building these big resiliency measures.
Subtitled "How Neddie Took the Train, Went to Hollywood, and Saved Civilization," the novel was about exactly that, and set in Los Angeles circa 1950 (nicely described as "a perfect combination of glamorous and crummy").
And This is Why We Can't Have Nice Things is about exactly that: the inability of Gillian Cosgriff to have proper grownup things without ruining them: see, lipstick, mobile phone etc. Jane Howard went to see this charming cabaret fringe show, which she gave a three-star review.
We were worried about exactly that pattern forming".
Perhaps, the following morning, when you can't really move and you're searching your cupboards for that leftover 5-HTP, you might enjoy learning about exactly that – the history of clandestine MDMA production.
One young man said: "I understand from this play that I should go out and do something, but I'm not quite clear about exactly what that is".
When I pressed them about what exactly that meant, Third Eye said something about cosmic energy and ayahuasca.
But there is disagreement about how exactly that will happen.
He doesn't, however, provide any finer details about what exactly that might entail.
But rarely does anyone ask any questions about what, exactly, that would entail.
