In-universe, the liberation of Kashyyyk occured in the year 4 ABY, 8 months after the Battle of Endor.
Out of universe, the novel Star Wars: Aftermath by Chuck Wendig, part of the Journey to Star Wars: the Force Awakens series, shows Han and Chewbacca embarking on their mission to liberate Kashyyyk:
"We've got an opportunity with a very small window."
Chewie gurgles and Han agrees: "Imra, like you said: I'm out of that life, so whatever it is you're bringing to me-"
She disappears and a new holo-image pops up: a planet.
It's Chewie's home.
A planet where Wookiees are still in thrall to the Empire. [...]
"They're gonna do ... who can say? A changing of the guards or something. Or they need ships for some planet or some other - I really don't know, Solo. The details are fuzzy, but what we do know is, the ships that are leaving won't immediately be replaced. Which means we have a few days."
Chewie raises his head back and howls.
"The Alliance - the New Republic, whatever they are - they got me on this thing. I've got a responsibility. I can't just change the plan and go off half-cocked...." And he knows what the New Republic will say. They have a strategy. They won't divert attention to Kashyyyk, not yet. He's asked. More than once.
Chewie is giving him this look. Not even making a sound. The Wookiee's chest is rising and falling.
And it hits Han: The words coming out of his mouth don't sound like him. Being out here, though, with Chewie, it's made him feel like he used to. They'd just go places. Do whatever they wanted. Follow their noses to drink and contraband and stacks of credits and whatever good or bad deeds came along.
A fire lights in Han's belly.
It's time to do this.
"Get everybody. Every right-thinking scamp, scoundrel, slicer, smuggler - anybody who owes me a favor. Anybody who hates the Empire like we do." [...] He turns to Chewbacca: "Hey, pal. You still know how to contact the other refugees? Roshyk, Hrrgn, Kirratha, and them?"
-- Star Wars: Aftermath
Less canonically, you may be interested in the history of the notion that Han and Chewbacca liberated Kashyyyk. This was first mentioned in the 2000 novel Agents of Chaos I: Hero's Trial by James Luceno:
[Chewbacca went on to become a soldierr in the New Republic,] Ralrra boomed and rumbled. [He aided in Kashyyyk's liveration afterr the Battle of Endorr. But he remained first and foremost devoted to Han Solo, as friend and indebted protectorr, and as guardian to Han Solo's spouse and three children.]
-- Agents of Chaos I: Hero's Trial
The next year, it was first shown in the Chewbacca campaign of the video game Star Wars: Galactic Battlegrounds. And the 2002 reference book The New Essential Guide to Characters's entry on Admiral Ackbar first named the conflict as the Battle of Kashyyyk.
(See the SW Wikia page.)